«* 


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University  of  California 


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Form  L-l 


This  book  is  DUE  on  the  last  date  stamped  below. 


APR  Z  i 
HOV"3'iTB23- 

D^C  14  1922 
MAR  31THI 


■ 


MAY  2  9  19 


DEC   8 

NOV  1 
DEC  5         <* 


JAN  1  8  1935 
FEB  6      1935 

&pR  2  4  1935 
?2\935 


5m-8,'21 


"UG6 


41 


— 


i  • 


LAWS  OF  WAGES 


THE  MACMILLAN   COMPANY 

NEW  YORK    •    BOSTON   •    CHICAGO 
SAN    FRANCISCO 

MACMILLAN   &  CO .,  Limited 

LONDON  •  BOMBAY  •  CALCUTTA 
MELBOURNE 

THE  MACMILLAN  CO.   OF  CANADA,  Ltd. 

TORONTO 


LAWS   OF   WAGES 


AN  ESSAY   IN   STATISTICAL  ECONOMICS 


BY 


HENRY   LUDWELL   MOORE 

PKOFESSOR   OF    POLITICAL   ECONOMY   IN   COLUMBIA 
UNIVERSITY 


"  II  progresso  dell'  Econoraia  politica  dipendera 
pel  futuro  in  gran  parte  dalla  ricerca  di  leggi  em- 
piriche,  ricavate  dalla  statistica,  e  che  si  parago- 
neranno  poi  colle  leggi  teoriclie  note,  o  che  ne 
faranno  conoscere  di  nuove."  Paketo 


Xrto  gorn 

THE   MACMILLAN   COMPANY 

1911 


All  rhjhtx  reserved 


3  4G^  8 


Copyright,  1911, 
By  THE   MACMILLAN  CO. 


Set  up  and  electrotyped.      Published  December,  ign. 


XortoooD  $reaa 

J.  8.  Clashing  Co.  —  Berwick  &  Smith  Co. 

Norwood,  Mass.,  U.S.A. 


TO 

JOHN  BATES   CLARK 

IX    ADMIRATION    AND    AFFECTION 
I    DEDICATE    THIS    ESSAY 


CONTENTS 


Introduction 


P  VI,  I. 

1 


CHAPTER   I 


STATISTICAL    LAWS 


A  Scatter  Diagram 

Definition  of  Terms 15 

Characteristics  of  Statistical  Laws 21 


CHAPTER   II 

WAGES,    MEANS    OF    SUBSISTENCE,    AND    THE   STANDARD 

OF    LIFE 

Description  of  Data 26 

Wages  and  the  Means  of  Subsistence 29 

Wages  and  the  Standard  of  Life  .....••  -^ 

Waives  of  Skilled  and  of  Unskilled  Laborers         ....  39 


CHAPTER  III 

WAGES    AND    THE    PRODUCTIVITY    OF    LABOR 

Description  of  Data        ......•••       45 

Fluctuations  in   the  Rate  of  Wages  and   in  the  Value  of  the 

Product / bl 

Fluctuations  in  the  Laborer's  Relative  Share  of  the  Product  and 

in  the  Ratio. of  Capital  to  Labor 55 

The  General  Trend  of  Wages 61 

vii 


viii  Contents 


CHAPTER   IV 


WAGES    AND    ABILITY 


PAfJK 


An  Hypothesis  as  to  the  Distribution  of  Ability  .         .         .         .74 

Grounds  for  the  Hypothesis 76 

The  Expression  of  the  Gaussian  Law  in  a  Form  that  will  facili- 
tate the  Testing  of  the  Differential  Theory  of  AVages  .         .  78 

The  Standard  Population 82 

The  Application  of  the  Theory  of  the  Standard  Population         .  85 

Remark  upon  the  Preceding  Demonstration         .         .         .  9o 


CHAPTER  V 

WAGES    AND    STRIKES 

Outcome  of  Strikes  as  affected  by  the  Strength  of  Trades-Unions  105 
Outcome  of  Strikes  as  limited  by  Economic  Law  .  .  .  121 
Summary 134 

CHAPTER  VI 

WAGES    AND    THE    CONCENTRATION    OF    INDUSTRY 

Wages  as  affected  by  the  Concentration  of  Industry  .  .  .  140 
Amount  of  Employment        .         .         .         .         .         .         .         .153 

Continuity  of  Employment 156 

Length  of  the  Working  Day 161 

* 

CHAPTER  VII 

CONCLUSIONS 

Statistical  Economics  and  Industrial  Legislation  .         .         .     169 

Practical  Aspects  of  the  Results  of  Preceding  Chapters  .  .  174 
Statistical  Economics  and  Synthetic  Economics  ....     196 


LAWS  OF  WAGES 


LAWS   OF   WAGES 


INTRODUCTION 

There  are  five  circumstances  the  coexistence  of 
which  at  the  present  time  will  probably  determine 
in  the  near  future  the  direction  and  character  of  such 
economic  investigations  as  shall  have  for  their  object 
the  discovery  of  general  facts  and  laws :  — 

(1)  The  pure  theory  of  economic  statics  has 
reached  a  definite,  mathematically  symbolic  form ; 
it  supplies  a  general  view  of  the  economic  field, 
and  indicates  the  desiderata  for  further  theoretical 
inquiries. 

The  utility  of  economic  theory  is  to  be  measured 
by  the  degree  in  which  it  solves  its  triple  task  of 
definition  and  analysis  of  concepts,  the  discovery  of 
appropriate  methods  for  handling  mutually  dependent 
social  phenomena,  and  the  presentation  of  a  general 
view  of  the  economic  field.  Clearness  and  precision 
of  definition  are  absolutely  indispensable  to  any  form 
of  quantitative  work.  So  long  as  economic  terms 
were  employed  with  the  vagueness  illustrated  by 
Jevons  when  he  showed  that  in  the  use  of  the  word 
"value"  three  distinct  meanings  were  habitually 
confused,  it  "  was  not  to  be  expected  that  we  could 
profitably    discuss    such    matters    as    economic    doc- 

B  1 


2  Laws  of  Wages 

trines."  *  The  net  result  of  the  subtle  discrimination 
and  criticism  of  concepts  which  has  characterized 
a  great  portion  of  contemporary  work  is  that,  for 
the  first  time,  the  inductive  worker  has  a  choice  of 
groups  of  terms  that  are  precise  and  clear. 

In  a  similar  manner,  in  quite  recent  years,  the 
idea  of  the  relations  of  economic  phenomena  has 
widened,  and  methods  have  been  discovered  that 
enable  us  to  visualize  these  interrelations  in  their 
complexity.  Economic  events  are  not  arrayed  in 
linear  connection,  the  one  event  following  the  other 
in  direct  series,  as  was  frequently  assumed  by  the 
classical  economists.  It  was  an  idle  controversy  that 
Malthus  and  Ricardo  conducted  upon  the  question 
whether  the  abundance  of  food  increases  the  popula- 
tion or  the  multitude  of  consumers  increases  the 
supply  of  food.  Social  phenomena  are  interrelated, 
are  mutually  dependent,  and  the  appropriate  method 
of  treating  such  a  form  of  interdependence  is  the  use 
of  a  system  of  simultaneous  equations  in  which  the 
equations  are  equal  in  number  to  the  unknown  quan- 
tities in  the  problem.  There  are  hints  of  this  con- 
ception in  the  works  of  the  earlier  economists ;  for 
example,  in  Cournot's  Recherches  sur  les  princijjes 
mathematiques  de  la  theorie  des  richesses,  but  it  was 
missed  by  Jevons,  as  was  shown  by  Professor  Marshall 
in  his  Academy  review  of  Jevons's  Tlieory  of  Political 
Economy.  Walras  introduced  it  in  an  important 
special  case  in  his  earlier  treatise.     It  has  received 

1  W.  S.  Jevons:   The  Theory  of  Political  Economy,  3d  edition,  p.  81. 


Introduction  3 

its  complete  development  in  Professor  Marshall's 
Principles  of  Economics  and  Professor  Pareto's  Cours 
cVeconomie  politique. 

The  third  part  of  the  task  of  the  economic  theory 
—  the  presentation  of  a  general  view  of  the  economic 
field  —  was  achieved  in  the  perfection  of  the  method 
of  simultaneous  equations  which  has  just  been  de- 
scribed. In  a  non-symbolic  form,  the  general  survey 
was  made  in  the  original  treatise  of  Professor  J.  B. 
Clark. 

(2)  Marxian  socialists  have  distinguished  between 
the  constructive  and  the  destructive  elements  of  their 
prophet's  teachings,  and  are  seeking  to  extend  the 
theory  of  socialism  through  the  development  of  the 
constructive  idea  in  the  light  of  concrete  data. 
The  real  beginning;  of  a  "scientific  socialism"  was 
in  Bernstein's  confession  :  "  Die  Fortentwicklung  und 
Ausbildung  der  marxistischen  Lehre  muss  mit  ihrer 
Kritik  beginnen.  Heute  stent  es  so,  dass  man  aus 
Marx  und  Eno-els  alles  beweisen  kann."1  It  was  a 
considerable  step  toward  "  industrial  emancipation " 
for  leading  socialists  like  Bernstein  and  Sorel  to 
recognize  the  vagueness,  inconsistency,  and  inade- 
quacy of  Marx's  teachings;  it  was  a  greater  stride 
in  the  same  direction  to  face  the  necessity  of  attack- 
ing anew  the  old  problems  and  to  decide  to  conduct 
further  inquiries  upon  the  basis  of  concrete  facts. 
The    newer    "  scientific   socialism "    will    rest   upon 

1  Ed.  Bernstein:  Die  Voraussetzungen  des  Sozialismus  und  die  Auf- 
g(d>en  der  Sozialdemokratie,  p.  19. 


4  Laws  of  Wages 

formulas  derived  from  experience :  "  Je  propose  de 
nommer  economie  concrete  la  science  moderne  qui  se 
fonde,  a  la  fois  sur  1' observation  directe  des  faits  et 
sur  la  connaissance  des  theories  abstraites  qui  lui 
permettent  de  comprendre  l'emploi  que  Ton  peut  faire 
des  concepts."1  The  aim  of  modern  theoretical  so- 
cialism thus  described  by  Sorel  is  the  aim  of  modern 
economics. 

(3)  The  growth  of  social  democracy  has  led  to 
measures  of  industrial  reform  whose  administration 
requires  the  periodic  collection  of  varied  statistics 
upon  a  large  scale.  Reforms  in  measures  of  taxation, 
where  the  reforms  are  genuine,  now,  for  the  first 
time,  give  a  definite  idea  as  to  the  amount  of  the 
wealth  of  nations  and  its  yield  of  earned  and  un- 
earned incomes.  Reforms  in  the  character  of  indus- 
trial insurance  and  in  government  reports  as  to  the 
condition  of  labor  now  give  detailed  information  as 
to  the  distribution  of  wages,  the  cost  of  living  among 
laborers,  the  causes  and  seasons  of  unemployment, 
the  relative  frequencies  and  causes  of  industrial  dis- 
putes, the  prevalence  of  diseases  among  workers,  and 
the  disabilities  of  old  age.  The  material  for  the 
concrete  treatment  of  economic  questions  is  being  ] 
supplied  yearly  in  increasing  abundance. 

(4)  The  problems  of  natural  science  have  required 
the  invention  of  a  calculus  of  mass  phenomena  that 
will  probably  yield  its  best  results  when  applied  to 
the   material  of  the  social  sciences.     The  wealth  of 

1  Georges  Sorel :  Introduction  a  V  economie  moderne,  p.  28. 


Introduction  5 

the  statistical  material  relating  to  economic  questions 
is  itself  a  source  of  embarrassment.  To  utilize  it 
for  scientific  purposes,  it  must  be  described  in  brief, 
summary  formulae,  and  these  formulae  must  be 
arranged  upon  a  plan  of  increasing  complexity  so 
that  it  will  be  possible  to  pass  from  accurate  descrip- 
tions of  mass  aggregates  to  the  relations  between 
the  aggregates  themselves.  Now,  concurrently  with 
the  development  of  economic  and  socialistic  theory 
and  the  increasing  supply  of  statistical  data,  the 
mathematical  instrument  for  rendering  the  statistical 
data  available  for  scientific  purposes  has  been  per- 
fected. The  calculus  of  mass  phenomena,  like  the 
infinitesimal  calculus,  owes  its  development  to  many 
workers,  but,  in  recent  years,  its  efficiency  has  been 
increased  by  the  labors  of  Professor  Pearson  and 
Professor  Edgeworth  far  more  than  during  the  whole 
period  intervening  since  the  days  of  Laplace  and 
Gauss.  There  is  reason  for  believing  that,  as  the 
science  of  statistics  had  its  origin  in  the  treatment 
of  social  questions,  so  likewise  the  newer  statistical 
methods  will  yield  their  most  important  results  when 
applied  to  social  data. 

(5)  The  perfection  of  mechanical  devices  for  per- 
forming mathematical  computations  has  rendered  it 
possible  for  individual  scientists  to  elaborate  the  new 
data  supplied  by  government  bureaus.  When  a 
science  is  iii  its  early  stages,  individual  scientists 
must  do  work  o{  many  kinds.  For  some  years  to 
come  all  essays  in  the  direction  of  connecting  economir 


6  Laics  of  Traces 

theory  with  economic  practice  must  be  tentative,  for 
the  investigator  must  at  the  same  time  master  the 
theory,  collect  the  facts,  and  take  from  them  their 
content  by  means  of  new  and  difficult  methods. 
With  the  mass  of  data  before  him,  the  task  would 
be  impossible  without  mechanical  aids  to  computa- 
tion. These  aids  are  being  supplied  in  increasing 
numbers  and  value  in  the  form  of  mathematical 
tables,  mechanical  tabulators,  and  arithmometers. 

In  the  following  chapters  I  have  endeavored  to 
use  the  newer  statistical  methods  and  the  more 
recent  economic  theory  to  extract,  from  data  re- 
lating to  wages,  either  new  truth  or  else  truth  in 
such  new  form  as  will  admit  of  its  being  brought 
into  fruitful  relation  with  the  generalizations  of 
economic  science. 

The  first  chapter  contains  a  description  of  the 
meaning  of  the  terms  representative  fact,  hypothesis, 
statistical  law,  which  are  the  principal  categories  by 
means  of  which  scientific  results  are  classified.  In 
order  to  secure  a  wise  expenditure  of  capital  and 
energy,  it  is  necessary  in  economic  science  as  in 
economic  affairs  to  make,  from  time  to  time,  an 
inventory  of  one's  possessions,  and  to  this  end  it  is 
all  important  that  there  should  be  no  ambiguity 
about  the  table  of  values  by  means  of  which  the 
inventory  is  effected.  In  particular,  we  economists 
should  recognize  the  truth  that,  throughout  a  very 


Introduction  7 

long  period  of  its  history,  our  science  has  been  con- 
cerned with  hypotheses  while  it  has  pretended  to  the 
discovery  of  laws. 

Having  defined  our  terms  and  illustrated  our 
method,  we  pass  to  the  consideration  of  economic 
theories  of  wages  in  the  light  of  existing  data  relat- 
ing to  the  income  of  laborers.  The  persistence  in 
economic  speculation  of  the  doctrines  of  wages  that 
are  associated  with  the  names,  respectively,  of  Turgot 
and  Ricardo  requires  that  the  statistical  economist 
should  measure,  if  he  can,  the  degree  of  truth  con- 
tained in  each  theory.  Data  are  now  available,  per- 
haps for  the  first  time,  upon  which  to  base  an 
inductive  investigation.  This  material  is  utilized 
to  measure  the  degree  of  relation  between  wages  and 
the  cost  of  the  means  of  subsistence,  and  between 
wa^es  and  the  standard  of  life  of  the  laborer. 

The  theory  according  to  wdiich,  under  perfect  com- 
petition, the  laborer  tends  to  receive  as  wages  the 
value  of  his  specific  product  is  one  phase  of  a  general 
theory  of  distribution  that  owes  its  development  to 
contemporary  economists.  It  will  not  be  denied, 
I  think,  that  one's  attitude  toward  theoretical  eco- 
nomics and  industrial  reform  should  be  greatly  affected 
by  the  outcome  of  an  inductive  test  applied  to  this 
doctrine.  The  theory  contains  two  principal  parts : 
(1)  as  to  the  trend  of  the  share  of  the  product  that 
goes  to  the  whole  class  of  laborers  in  the  form  of 
general  wages,  and  (2)  as  to  the  law  of  the  distri- 
bution of  general  wages  among  the  subgroups  form- 


8  Laws  of  Wages 

ing  the  laboring  class.  These  two  parts  of  the 
productivity  theory  of  wages  I  have  subjected  to 
statistical  treatment. 

Owing  to  the  fact  that  the  productivity  theory 
was  developed  by  economists  who  employed  the 
device  of  a  static  state  to  facilitate  the  working  of 
their  isolated  hypotheses,  it  has  been  assumed  by 
sympathetic  critics  that  its  validity  is  limited  to  a 
hypothetical  static  state.  This  criticism  must  be 
withdrawn  if  it  can  be  shown  that  the  theory  sup- 
plies the  clue  to  the  explanation  of  a  concrete,  highly 
dynamic  phenomenon  of  the  first  importance.  What 
light  can  the  productivity  theory  of  wages  throw 
upon  the  scientific  problem  of  the  economic  laws 
of  strikes  and  their  outcome  ?  To  answer  this  ques- 
tion the  first  obvious  desideratum  is  the  proof  that 
strikes  and  their  outcome  are  subject  to  law ;  it  will 
then  be  time  to  inquire  whether  the  observed  regu- 
larities are  explicable  by  means  of  the  productivity 
hypothesis. 

Of  at  least  equal  importance  with  the  question  of 
the  relation  of  strikes  to  wages  is  the  consideration 
of  the  effects  upon  the  condition  of  the  laborers  of 
the  concentration  of  industry  in  large  establishments. 
It  will  be  shown,  for  example,  that  the  mean  rate 
of  wages  in  the  textile  industries  tends  to  increase 
with  the  size  of  the  establishment.  But  what  shall 
be  the  interpretation  of  this  result  ?  Shall  the  infer- 
ence be  that  the  more  highly  organized  technical 
equipment  of  the  larger  establishments  results  in   a 


Introduction  <) 

higher  effective  productivity  of  the  laborer,  which 
finds  its  expression  in  a  larger  wage?  Or  may  it 
not  be  that  the  great  industrial  machines  select  the 
ablest  laborers  at  the  age  when  they  are  most  pro- 
ductive, and  then,  after  the  very  best  of  their  lives 
has  been  exploited,  throw  them  out  of  the  industry 
to  find  their  support  elsewhere  ?  The  law  of  the 
variation  of  wages  with  age,  in  the  general  industry 
and  in  the  large  establishments,  will  give  light  upon 
this  problem.  The  high  mean  wages  of  large  estab- 
lishments may  be  spurious  averages  due  to  the  differ- 
ent ages  of  the  populations  in  large  and  in  small 
establishments.  The  real  social  gain  or  loss  resulting 
from  the  concentration  of  industry  can  be  measured 
only  after  the  consequences  have  been  apprehended 
of  the  selective  process  that  concentration  entails. 

In  a  concluding  chapter,  the  general  results  of  the 
essay  are  summarized  with  the  purpose  of  consider- 
ing their  bearing  upon  the  problem  of  the  organiza- 
tion of  industry.  It  is  hoped  that,  supported  as  they 
are  by  economic  theory  and  inductive  verification, 
they  may,  in  their  degree,  add  to  the  positive  knowl- 
edge that  shall  be  utilized  in  the  control  of  the  eco- 
nomic changes  that  follow  upon  our  increasing  wealth 
and  population. 


CHAPTER   I 

STATISTICAL   LAWS 

"  En  general,  une  theorie  scientifique  quelconque,  imaginee  pour 
relier  un  certain  nombre  de  faits  trouves  par  l'observation,  peut  etre 
assimilee  a  la  courbe  que  Ton  trace  d'apres  une  definition  mathe'ma- 
tique,  en  s'imposant  la  condition  de  la  faire  passer  par  un  certain 
nombre  de  points  donne"s  d'avance.  Le  jugetnent  que  la  raison  porte 
sur  la  valeur  intrinseque  de  cette  theorie  est  un  jugement  probable, 
dont  la  probability  tient  d'une  part  a  la  simplicity  de  la  formule 
the"orique,  d'autre  part  au  nombre  des  faits  ou  des  groupes  de  faits 
qu'elle  relie."  —  Cournot. 

The  statistical  economist  is  concerned  with  eco- 
nomic facts,  hypotheses,  and  laws.  He  begins  his 
investigations  with  the  assembling  of  facts,  and  seeks 
through  the  mediation  of  hypotheses  to  arrive  at 
laws.  As  economist,  his  aim  is  to  throw  the  great- 
est possible  light  upon  the  relation  of  the  economic 
facts  before  him,  and,  as  scientist,  he  expects  to 
achieve  this  end  by  summarizing  the  descriptions  of 
the  relations  of  facts  in  the  simplest  and  most  gen- 
eral formulae  possible.  Equipped  with  new  and 
powerful  instruments  of  research,  he  approaches  his 
task  in  a  precise,  systematic  way  that  yields  results 
in  a  much  more  definite  and  usable  form  than  the 
inspiring  generalizations  of  the  early  masters  of  the 

science. 

What,  precisely,  was  the  meaning  of  Adam  Smith  in 

10 


Statist/ nil   LaiVS  11 

his  enumeration  of  the  following  circumstances  in  con- 
nection with  the  discussion  of  the  inequalities  in  wages? 
'•  First,  the  agreeableness  or  disagreeableness  of  the 
employments  themselves;  secondly,  the  easiness  and 
cheapness,  or  the  difficulty  and  expense  of  learning 
them  ;  thirdly,  the  constancy  or  inconstancy  of  employ- 
ment in  them  ;  fourthly,  the  small  or  great  trust  which 
must  be  reposed  in  those  who  exercise  them ;  and  fifthly, 
the  probability  or  improbability  of  success  in  them." 
Did  he  mean  that  these  factors  are  always  present  as 
causes  of  inequalities  in  wages,  that  they  are  of  equal  im- 
portance, and  that  wages  vary  in  either  direct  or  inverse 
ratio  with  their  several  variations  ?  Or,  was  not  his 
meaning,  rather,  that  the  enumerated  factors  are  so  many 
possible  hypotheses,  one  or  more  of  which,  in  particular 
cases,  may  give  the  clue  to  the  observed  inequality  in 
wagss  ?  Before  it  would  be  allowable  to  speak  of  a  law 
of  wages,  in  any  particular  case,  it  would  be  necessary  to 
show  not  only  that  wages  vary  with  the  assumed  factor, 
but  to  derive  the  formula  of  the  variation  and  to  meas- 
ure the  degree  of  association  between  the  phenomena. 
It  will  contribute  to  the  better  understanding  of 
the  nature  of  the  results  in  subsequent  chapters  to 
consider  here  the  meaning  of  the  terms :  general  or 
representative  fact,  hypothesis,  statistical  law. 

In  the  accompanying  Figure  1  the  details  of  a 
"scatter  diagram  "  '  are  depicted.  A  scatter  diagram 
is  a  graphic  description  of  the  quantitative  relation 

1  A  term  due  to  Professor  Pearson. 


12 


Laws  of  Wages 


§ 


&      §      §      5      §      $      §      § 


Statistical   Lairs 


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S  I  I  \\   HSd   s:i\  IH'd    «,!    H3W0M    .1"   -  r^   \\     i-.\:ia.\v 

~ 

14  Lcnvs  of  Wages 

between  two  series  of  facts.  In  this  particular  case 
the  two  groups  of  facts  are  the  average  wages  of  men 
and  the  average  wages  of  women,  in  the  several  states 
and  territories  of  the  United  States.1  The  scatter 
diagram  is  constructed  by  measuring  in  sequence 
upon  the  horizontal  line  the  tabular  values,  for  the 
several  states  and  territories,  of  the  average  wages  of 
men,  and  then  plotting  perpendicularly  to  these  values 
the  corresponding  average  wages  of  women.  Each 
pair  of  related  values  is  represented  by  a  point  upon 
the  diagram.  For  example,  in  case  of  Montana, 
the  average  wage  of  men  was  $18.00  a  week,  and  the 
corresponding  wage  for  women  was  $8.60.  This 
relation  is  indicated  by  the  extreme  point  in  the 
upper  right-hand  corner  of  the  diagram. 

The  next  stage  in  the  construction  of  the  scatter 
diagram  is  represented  by  the  series  of  small  circles 
that  are  connected  by  a  broken  line.  The  facts  upon 
which  this  part  of  the  construction  rests  are  given  in 
Table  I.  The  individual  observations  are  not  dealt 
with  directly  as  they  are  indicated  upon  the  diagram, 
but  they  are  grouped  into  arrays  the  characteristics 
of  which  are  summarized  in  averages  and  then  repre- 
sented upon  the  diagram  by  circles.  For  example, 
in  the  states  in  which  the  average  wages  of  men  were 
between  $10  and  $11  a  week,  the  corresponding 
wages  of  women  formed  an  array  whose  average 
value  was   $5.60.     This  representative  value  of  the 

1  The  data  are  taken  from  the  Census  of  Manufactures,  190"), 
Bulletin  93,  p.  36. 


Statistical  Laws  15 

array  is  indicated  by  the  circle  placed  above  the  point 
$10.50,  at  a  distance  from  the  horizontal  line  corre- 
sponding to  $5.60  on  the  perpendicular  scale.  The 
circles  are  connected  by  a  broken  line. 

Suppose,  now,  that  the  particular  problem  to  be 
investigated  is  the  relation  between  the  wages  of  men 
and  the  wages  of  women.  From  the  general  sweep 
of  the  scatter  diagram  one  would  say  that  the  two 
(plant  ities  are  related.  But  what  is  the  exact  nature 
of  the  function  descriptive  of  the  relation,  and  what 
is  the  degree  of  association  between  the  wages  of  men 
and  the  wages  of  women?  The  attempt  to  give 
definite  answers  to  these  questions  will  lead  to  a 
specific  instance  of  the  exact  use  of  the  terms :  gen- 
eral fact,  hypothesis,  statistical  law. 

The  series  of  points  upon  the  scatter  diagram  is 
simply  a  graphical  transcript  of  a  double  entry  table 
recording  the  series  of  related  measurements.  But 
where  the  observations  mount  into  hundreds  and 
thousands,  it  would  be  extremely  laborious  to  consider 
directly  the  more  or  less  accidental  position  of  each 
point,  and  still,  in  giving  a  summary  description  of 
the  relation  of  two  series  of  values  —  which  is  the 
object  of  the  investigation  —  it  is  not  allowable  to 
neglect  the  singularity  of  any  point.  Each  point 
must  have  a  weight  in  the  investigation  that  is  pro- 
portional to  its  importance. 

Now,  in  any  investigation,  the  general,  or  represen- 
tative, fact  is  that  fact  which  for  the  purpose  in  hand 
conveys  the  maximum  of  information  about  the  group 


16  Laws  of  Wages 

it  represents.  In  the  problem  before  us,  the  arith- 
metical averages  x  of  the  items  in  the  several  arrays 
are  regarded  as  representative  of  their  respective 
groups.  By  substituting  representative  observations 
for  the  individual  observations,  the  number  of  points 
to  be  treated,  in  the  case  under  consideration,  is 
reduced  from  fifty  to  twelve. 

What  is  the  law  of  the  association  of  the  represent- 
ative points?  The  answer  to  that  question  is  depend- 
ent upon  the  finding  of  the  simplest  curve  that  will 
fit  satisfactorily  the  given  representative  points.  An 
hypothesis  must  be  made  as  to  the  nature  of  the 
curve  that  will  satisfy  the  imposed  conditions  of 
simplicity  and  excellence  of  fit,  and  the  hypothesis 
must  then  be  tested  by  the  representative  facts. 
Until  this  test  has  been  applied,  there  is  no  ground 
of  preference  for  any  particular  hypothesis  over  an 
infinite  number  of  other  possible  suppositions  as  to  the 
relation  of  the  series  of  phenomena  under  observation. 

Incidentally  it  may  be  observed  that  the  ideas 
"simplicity"  and  "  excellence  of  fit"  do  not  admit  of 
rigid  general  definition.  According  to  the  point  of 
view,  a  given  curve  may  be  either  simple  or  complex : 
its  formula  may,  for  example,  have  few  constants 
and  for  that  reason  be  regarded  as  simple,  but  the 
computation  of  the  constants  may  involve  the  use  of 
extremely  intricate  processes,  which  would  more  than 
offset  the    simplicity    due    to  the    small    number  of 

1  For  certain  classes  of  problems  it  might  be  desirable  to  use  other 
forms  of  representative  values,f  or  example,  the  mode  or  median  of  arrays. 


Statistical  Laws  17 

constants.  A  particular  curve  may  be  regarded  as 
simple  and  appropriate  to  given  conditions  because 
of  its  consonance  with  a  priori  theory,  or  its  sim- 
plicity may  rest  entirely  upon  the  facility  with  which 
it  lends  itself  to  analytical  treatment.  Similar  obser- 
vations may  be  made  with  regard  to  the  idea  of  excel- 
lence of  fit.1 

Returning  to  the  problem  of  the  quantitative  relation 
between  the  wages  of  men  and  the  wages  of  women, 
we  inquire  whether  the  straight  line  upon  the  scatter 
diagram  or  some  other  curve  not  appearing  upon  the 
chart  is  the  law  of  the  relation  between  the  wages  of 
men  and  the  wages  of  women.  The  query  leads  to 
the  definition  of  the  term  statistical  law.  The  statis- 
tical law  of  the  association  of  two  series  of  facts  is 
the  hypothesis  that  satisfies  best  the  imposed  condi- 
tions of  simplicity  and  excellence  of  fit  to  the  repre- 
sentative facts.  The  straight  line  in  the  scatter  diagram, 
the  equation  to  which  is  y  =  .3829  x  +  1.5204,  satisfies 
the  Pearsonian  test '  of  excellence  of  fit,  and  is  there- 
fore regarded  as  the  statistical  law  of  the  association 
of  the  money  wages  of  men  and  the  money  wages  of 
women.  It  may  be  said  definitely  that  on  the  average, 
in  the  case  before  us,  a  variation  of  one  dollar  in  the 
wages  of  men  is  associated  with  a  variation  of  about 
38  cents  in  the  wages  of  women. 

1  A  more  detailed  discussion  of  these  ideas  is  given  in  the  article 
'•The  Statistical  Complement  of  Pure  Economics."  Quarter!;/  Journal 
of  Economics,  November,  1908. 

2  Philosophical  Magazine,  July,  1900,  pp.  157-175.  Biometrika,  1002, 
pp.  155-10:$. 


18  Laws  of  Wages 

What  is  the  measure  of  the  degree  of  association 
between  the  money  wages  of  men  and  the  money 
wa^es  of  women  ?  The  above  formula,  as  we  have 
observed,  conveys  the  information  that  upon  the 
average  a  variation  of  one  dollar  in  the  wages  of 
men  is  associated  with  a  variation  of  about  38  cents 
in  the  wages  of  women.  But  does  a  variation  of  38 
cents  in  the  wages  of  women  bear  the  same  propor- 
tion to  the  total  variation  of  the  wages  of  women 
that  a  variation  of  one  dollar  in  the  wages  of  men 
bears  to  the  total  variation  of  the  wages  of  men  ? 
In  order  that  an  abstract  number  expressing  the 
measure  of  correlation  between  the  two  series  of  facts 
may  be  obtained,  the  associated  variations  must  be 
expressed  in  terms  of  units  that  measure  the  respec- 
tive variabilities  of  the  two  groups  of  facts. 

The  law  of  the  associated  variation  is  y=  .3829  x  + 
1.5204,  where  the  origin  of  the  coordinates  is  at 
zero.  If  the  origin  be  transferred  to  the  mean  of  the 
system  of  points,  that  is,  to  the  point  the  coordinates 
of  which  are  the  mean  of  the  wages  of  men  and  the 
mean  of  the  wages  of  women,  the  equation  becomes 
?/  =  .3829x.  If,  now,  the  standard  deviation  of  the 
wages  of  men  be  represented  by  <rx,  and  the  standard 
deviation  of  the  wages  of  women,  by  cr2,  the  equation 

may    be    written    y  =  r  —  x,  or   -^-=r — ,    wThere    r, 

which  is  the  coefficient  of  correlation,  measures 
the  degree  of  association  between  the  variation  in 
the  money  wages  of  men  and  the  money  wages  of 


Statistical  Laws  19 

women,  the  variations  being  expressed  in  terms  of 
the  standard  deviations  of  the  respective  groups. 
But,  in  the  particular  case  before  us, 

r ^  =  .3829  and  a,  =  2.0915,  cr,=  1.1898. 

Therefore  r=  M^f  (-8829)  =  -86G' 

The  coefficient  of  correlation  varies  between  the 
limits  ±1.  When  r—  ±1,  the  correlation  between 
the  associated  variations  of  the  phenomena  is  per- 
fect. When  r  =  o,  there  is  no  linear  correlation. 
Intermediate  values  of  r  express  the  degrees  of  asso- 
ciation between  the  series  of  phenomena. 

Inasmuch  as  the  coefficient  of  correlation,  r,  is  an 
abstract  number  that  is  independent  of  the  concrete 
units  in  which  the  phenomena  are  expressed,  it  makes 
possible  the  comparison  of   the  degree  of  association 
between  series  of   phenomena  that  are  qualitatively 
different.     For  example,  it  may  be  proved  that  the 
wages  of    skilled  laborers  vary   with  the  wages  of 
unskilled  laborers,  and   it  may  likewise    be    shown 
that   the  wages  of  skilled   laborers  vary  with   their 
standard  of  life.     But  in  each  case,  what  is  the  law 
of  variation  and  what  is  the   degree  of  association 
between  the  two  variables  ?     Are  the  wages  of  skilled 
laborers  more  closely  connected   with   the   wages   of 
unskilled  laborers  than  with  their  own  standard  of 
life  ?     The  appropriate  coefficients  of  correlation  give 
the  answers  to  these  questions,  as  we  shall  see,  in  the 
next  chapter. 


20  Laws  of  Wages 

We  have  now  a  very  concrete  and  definite  idea  of 
representative,  general  facts,  hypotheses,  and  statistical 
laws.  By  a  progressive  synthesis  a  statistical  investi- 
gation passes  from  individual  observations  to  represent- 
ative facts  and  from  representative  facts  to  statistical 
laws.  The  representative  facts  exhibit  the  charac- 
teristics of  the  individual  observations  which,  for  the 
purpose  in  hand,  are  most  useful.  The  statistical 
law  summarizes  in  the  simplest  possible  formula  the 
information  conveyed  by  the  representative  facts. 

The  meanings  of  these  terms  in  the  theory  of  statis- 
tics have  a  general  resemblance  to  their  usage  in  the 
other  sciences.  For,  a  theory  or  hypothesis  as  to  the 
association  of  given  facts,  in  any  department  of 
knowledge,  may  be  likened  to  an  hypothesis  as  to  the 
simplest  form  of  curve  that  will  pass  as  nearly  as 
possible  to  given  points.  In  each  case  the  individual 
observations  —  the  facts  and  the  points  —  fall  into 
groups  that  may  be  described  by  typical,  representa- 
tive facts.  The  hypothesis  or  theory  in  each  case 
is  the  supposition  as  to  the  nature  of  the  relation 
of  the  representative  facts.  The  law  of  the  facts 
and  of  the  points  is  the  supposition  that  satisfies 
best  the  accepted  standard  of  simplicity  and  ex- 
cellence of  fit  of  the  facts  to  the  hypothesis.  Before 
any  theory  is  accepted  as  the  appropriate  explana- 
tion of  the  phenomena,  proof  must  be  submitted 
that  the  facts  which  it  purports  to  describe  are 
representative  facts  and  that  it  satisfies  the  approved 


Statistical  Laws  '2\ 

test  of  simplicity  and  excellence  of  fit  to  the  general 
facts. 

But  added  to  the  common  idea  in  the  general  use 
of  these  terms,  there  arc  special  characteristics  in 
case  of  statistical  laws  that  must  be  discriminated. 
The  inductive  laws  that  are  estahlished  by  means  of 
statistical  methods  in  the  social  sciences  are  — 

(1)  Laws  of  mass  phenomena. 

In  order  to  arrive  at  the  conception  of  statis- 
tical law  that  has  been  described  in  this 
chapter,  we  summarized  the  characteristics 
of  groups  of  phenomena  by  means  of  repre- 
sentative facts,  and  then  proceeded  to  test 
the  hypothesis  as  to  the  relation  of  the 
general  facts  by  means  of  a  conventional 
standard  of  simplicity  and  excellence  of  fit. 
As  the  test  is  applied  with  reference  to  the 
general  facts,  the  law  is,  in  reality,  the  law 
of  the  general  facts :  its  validity  is  limited 
to  the  general  facts  and  need  not  apply  to 
the  ^particular  instances.  For  example,  a 
knowledge  of  the  law  of  mortality  will  not 
enable  one  to  predict  that  X.  aged  forty 
years,  will  die  in  a  given  year.  The  law, 
however,  docs  yield  the  necessary  information 
for  predicting  the  average  proportion  of  those 
now  living  who  will  die  in  successive  years. 

(2)  Laws  the  strict  validity  of  which  is  limited   to 

a  particular  time  and  place. 


22  Laws  of  Wages 

A  statistical  social  law  is  a  summary  descrip- 
tion of  the  resultant  of  many  independent 
factors  whose  combination  varies  in  time 
and  place.  The  statistical  law  of  the  varia- 
tions of  price  with  the  supply  of  a  com- 
modity has  one  form  in  a  highly  competitive 
center  and  quite  a  different  form  in  an  agri- 
cultural community. 

(3)  Laws  the  strict  validity  of  which  does  not  ex- 

tend beyond  the  limits  of  observation. 
A  statistical  law  of   inheritance  derived  from 
the   investigation   of   a  population    varying 
between    the    normal    limits    should  not  be 
assumed  to  apply  to  dwarfs  and  giants. 

(4)  Laws  the  generality  of  which  ranges  from  an 

empirical  summary  of  the  quantitative  rela- 
tion between  series  of  facts  of  a  particular 
time  and  place  to  an  inductive  verification 
of  a  general  theorem  of  a  priori  science. 
It  would  be  easy  to  establish  that,  in  a  partic- 
ular country,  at  a  given  time,  the  average 
wage  of  laborers  varies  in  direct  relation 
with  the  density  of  the  population.  But 
such  a  law  of  association  is  simply  an  em- 
pirical law.  If  we  extended  our  investiga- 
tion to  different  times  and  places,  we  should 
expect  to  find  a  great  variation  in  the  de- 
grees of  association  of  the  two  phenomena. 
But  suppose  that  the  productivity  theory  of 
wages  should  receive  inductive  verification 


Statistical  Laws  23 

in  a  particular  instance.  In  that  case  the 
confidence  in  the  generality  and  the  stabih  y 
of  the  results  would  be  far  greater  because 
of  the  added  weight  of  the  a  priori  demon- 
stration. 

It  has  been  frequently  assumed,  even  by  econo- 
mists, that  pure  economics,  concerned  as  it  is  with 
general  theories,  can  have  but  scant  relation  to  the 
varying  succession  of  particular  instances  of  concrete 
life.  And,  indeed,  it  is  sometimes  regarded  as  futile 
to  attempt  to  bring  the  two  into  factual  relation. 
But  there  can  be  little  doubt  that  the  despairing  note 
is  due  to  our  ignorance  of  the  empirical  laws  that 
bind  together  the  whole  social  organism.  A  definite 
conception  of  the  character  and  strength  of  these 
binding  ties  must  lead  to  a  perception  of  the  direct 
connection  between  pure  theory  and  concrete  life. 

Statistical  economics,  in  which  the  following 
chapters  are  essays,  proposes  this  twofold  object: 
(1)  to  bring  to  the  test  of  representative  facts  the 
hypotheses  and  theorems  of  pure  economics  ;  (2)  to 
supply  data,  in  the  form  of  general  facts  and  empiri- 
cal laws,  for  the  elaboration  of  dynamic  economics. 


CHAPTER   II 

WAGES,   MEANS   OF   SUBSISTENCE   AND   THE   STAND- 
ARD  OF   LIFE 

"  The  natural  price  of  labour,  therefore,  depends  on  the  price  of 
the  food,  necessaries,  and  conveniences  required  for  the  support  of 
the  labourer  and  his  family."  "  It  is  not  to  be  understood  that  the 
natural  price  of  labour,  estimated  even  in  food  and  necessaries,  is 
absolutely  fixed  and  constant.  It  varies  at  different  times  in  the 
same  country,  and  very  materially  differs  in  different  countries." 

—  RlCARDO. 

Three  aspects  of  the  remuneration  of  labor  have 
each,  at  different  times,  so  engaged  the  attention 
of  economists  as  to  lead  to  three  different  theories 
of  wages  :  the  theory  of  the  dependence  of  wages 
upon  the  means  of  subsistence;  the  theory  of  their 
dependence  upon  the  standard  of  life  ;  and  the  theory 
of  their  dependence  upon  the  laborer's  economic  pro- 
ductivity. 'The  special  conditions  of  the  times  in 
which  these  hypotheses  had  their  origin  were  doubt- 
less responsible  for  the  distorted  perspective  exhibited 
in  the  various  attempts  to  state  a  scientific  theory 
of  the  laborer's  income.  In  recent  years  there  has 
been  a  disposition  to  recognize  that  each  of  the 
partial  sketches  contains  an  element  of  truth,  but  the 
de°ree  of  truth  in  each  has  not  been  measured,  and 
consequently  it  has  not  been  possible  to  weave  into  a 
satisfactory  whole  the  elements  supplied  by  the 
several  theories. 

24 


Means  of  Subsistence  and  the  Standard  of  Life     25 

"  The  general  tendency  of  wages  since  the  intro- 
duction of  power  machinery  and  the  employment 
of  women  and  children  in  its  operation  has  been 
upward,  but  it  will  be  difficult  to  decide  positively 
whether  such  increase  is  due  absolutely  to  the  use 
of  machinery  or  to  a  higher  standard  of  living,  or 
to  the  increased  productivity  of  labor  supplemented 
by  machinery,  or  to  all  these  causes  combined,  or  to 
other  causes.  .  .  .  This  phase  of  the  subject  there- 
fore involves  too  much  speculation  for  a  thoroughly 
statistical  presentation ;  the  method  can  be  only 
suggestive  of  the  arguments  which  might  be  used 
for  or  against  the  use  of  machinery  because  of  its 
effect  on  wages."  * 

To  accept  this  view  of  the  problem  of  wages  and 
of  the  limitations  of  the  statistical  method  would 
be  to  abandon  the  hope  of  solving  one  of  the  most 
important  problems  of  industrial  life.  Indeed,  if 
the  power  of  the  statistical  calculus  does  not  suffice 
to  analyze  this  problem  into  its  constituent  elements, 
then  all  effort  in  the  direction  of  a  concrete  science 
of  economics  is  vain  ;  for  all"  the  fundamental  prob- 
lems of  the  science  present  similar  degrees  of  com- 
plexity. 

Instead  of  seeking  a  unique  solution  of  the  wages 
question  in  an  a  j/ri<>ri  way,  we  shall  approach  the 
concrete  problem  by  attempting  to  find  statistical 
answers  to   several    important   questions   related    to 

1  Thirteenth  Annual  Report  of  the  Commissioner  of  Labor,  for  the 
United  States,  1898,  Vol.  i,  p.  5. 


26  Laws  of  Wages 

the  subject  of  this  chapter.     In  the  following  chap- 
ters other  aspects  of  the  problem  will  be  investigated. 
Do    wages   vary    with    the    cost  of  the  means  of 
subsistence,  and,  if  so,  what  is  the  law  of  the  vari- 
ation and  what  is  the  measure  of  the  correlation  in 
the  variation  ?     Do  wages  vary    with    the   standard 
of  life,  and,  if  so,  what  is  the  law  of  the  variation 
and  the  degree  of  the  correlation  ?     Are  wages  more 
directly  affected    by    the  cost  of  the  means  of  sub- 
sistence  than   by    the    standard    of    life  ?      Do    the 
answers  to  these  questions  differ   according   as    the 
wao-es    of    skilled    or    of   unskilled   labor   are   under 
investigation?     Is  there    any   relation   between    the 
variation  of  the  wages  of  skilled  labor  and  the  wages 
of  unskilled  labor  ?     If  there  is  such  a  relation,  how 
does   the   degree   of   correlation    compare    with    the 
correlation  of  wages  with  the  cost  of  the  means  of 
subsistence  and  with   the    standard   of  life?     These 
are  some  of  the  very  critical  questions  affecting  the 
theory  of  wages  that  need  to  be  treated  in  an  induc- 
tive way. 

Description  of  Data. 

Table  I,  in  the  Appendix  to  this  chapter,  embodies  a 
valuable  collection  of  material  relating  to  the  means 
of  subsistence,  the  standard  of  life  and  wages.  It  is 
drawn  from  the  monumental  report  on  Salaires  et 
duree  du  travail  dans  I Industrie  francaise  which  was 
published,  in  1893-1897,  by  the  French  Office  du 
Travail.     It  has  the    advantage  of  having  been  col- 


Means  of  Subsistence  and  the  Standard  of  Life     '21 

lected  and  compiled  by  a  single  authority  and  of 
covering  87  separate  departements,  thus  insuring, 
through  the  method  and  simultaneity  of  the  collection 
of  data,  an  unusual  comparability  of  results,  and, 
through  the  scope  of  the  investigation,  an  adequacy 
of  material  for  scientific  generalization. 

In  column  I,  the  87  departements  of  France  are 
enumerated.  In  columns  II  and  III,  the  mean  wages 
respectively  of  unskilled  and  of  skilled  laborers  are 
given.  The  raw  material  upon  which  the  means  are 
based  was  obtained  from  the  conseils  de  pruoV  hommes, 
in  189G.  The  means  given  for  manamvres,  or  unskilled 
laborers,  are  derived  from  the  wages  of  jour nailers  and 
trrrnssiers,  and  the  means  for  skilled  laborers  (Vouvrier 
de  metier  ordinaire)  are  the  averages  for  the  following 
trades:  compositeur  a  i mprimerie,  cordonnier,  tailleurs 
d1 habits,  cliirron,  marichal f errant, plombier,  macon.1 

In  column  IV  is  tabulated  for  each  departement  a 
"  coefficient  de  depense  en  objets  a" alimentation  et 
de  chauffage,''which  will  be  referred  to,  in  the  argument 
later  on,  as  the  cost  of  the  means  of  subsistence.  The 
figure  given,  in  case  of  each  departement,  represents 
the  cost  in  that  departement  of  definite  quantities  of 
selected  commodities  that  are  regarded  as  sufficient  to 
sustain,  for  one  year,  a  family  of  six  members  three 
of  whom,  on  the  average,  are  at  work.  The  prices 
that  enter  into  the  estimate  of  the  costs  are  wholesale 
prices  that  were  paid  in  the  respective  dipartenn  nts,  in 

1  Salaires  et  dure'e  du  travail  dans  I'industru  francaise,  Vol.  IV,  pp. 
225,  239,  240, 


i-N  Laws  of  Wages 

1803,  by  representative  institutions,  such  as  schools 
and  hospitals.  The  kinds  of  commodities  making  up 
the  laborer's  budget  were  selected  by  the  Office  du 
Travail  after  having  examined  the  series  of  index 
numbers  previously  used  in  other  investigations  in 
France.  An  actual  record  of  expenditures  by  14 
families  of  weavers,  composed  of  six  members  three 
of  whom,  on  the  average,  were  at  work,  formed  the 
basis  for  the  estimate  as  to  the  portions  in  which  the 
several  commodities  should  enter  into  the  index 
number.  It  is  to  these  weaver  budgets  that  reference 
is  made  in  the  French  report  as  to  the  principles  that 
were  followed  in  composing  the  standard  :  "  nous  pren- 
drons  simplement  pour  base  de  la  depense,  en  objets 
a" alimentation,  des  quantites  exprimees  en  chiffres  ronds, 
de  telle  maniere:  (1)  que  ces  quantites  soient  effectivement 
capables  a" assurer  V existence  de  6  personnes,  par  exam- 
ple ;  (2)  que  la  repartition  de  la  depense  qui  en  resulte 
ne  secarte  pas  trop  de  celle  rapportee  ci-dessus.,y  1 

The  figures  in  column  IV  represent,  therefore,  the 
relative  costs  in  the  several  departements  of  fixed 
means  of  subsistence.2 

1  Salaires  et  dure'e  du  travail  dans  V Industrie  franraise,  Vol.  TV,  p.  251 . 

2  The  kinds  and  quantities  of  the  commodities  are  tabulated  in 
Vol.  IV,  p.  252. 

In  criticism  of  this  standard  budget,  it  may,  of  course,  be  objected 
that  retail,  instead  of  wholesale,  prices  should  have  been  used.  Rut 
the  Office  du  Travail  resorted  to  the  use  of  wholesale  figures  only  after 
the  failure  of  the  attempt  to  secure  satisfactory  retail  prices.  Besides, 
the  wholesale  figures  were  regarded  by  the  Office  du  Travail  as  being 
fairly  representative  of  the  local  variations  of  retail  prices  in  France. 

It  is  to  be  regretted  that  an  error  of  unknown  magnitude  was  in- 
troduced in  the  effort  to  compensate  for  the  relatively  low  wholesale 


Means  of  Subsidence  and  the  Standard  of  Life     29 

Column  V  contains  for  each  departement,  the  daily 
" prix ordinaire  de  pension  paye"  par  Vouvrier  is<>l<'  pom- 
le  logement  et  lanourriture."  In  the  subsequent  argu- 
ment, this  column  will  be  referred  to  as  being  repre- 
sentative of  the  cost  of  the  standard  of  life.1  Column 
V  differs  from  column  IV  in  that  the  prix  de  pension 
is  representative  of  a  standard  that  varies  in  kind 
and  quantity,  as  well  as  in  prices,  from  departerm  nt  to 
departement,  while  column  IV  simply  records  the  de- 
part mental  prices  of  a  fixed  mode  of  subsistence. 
The  figures  were  obtained,  in  1896,  from  the  conseils 
de  prudliommes? 

With  this  description  of  our  data,  we  may  now 
enter  upon  an  investigation  of  the  interdependence 
of  the  several  factors  that  have  been  described. 

Wages  and  the  Means  of  Subsistence. 

In  its  crassest  form  the  doctrine  that  wages  are  de- 
termined by  the  means  of  subsistence  of  the  laborer 
was  formulated  by  Turgot.     "  En  tout  genre  de  travail 

prices  by  increasing  the  quantities  of  commodities.  "  Comme  les  prix 
qui  servient  de  bast  nn.r  < "/< •'//.-•  li-apres  sont  des  prixde  gros,nous  avons  ades- 
sein  plutot  force  les  quantite's  a  multiplier  par  ces  prix,  de  telle  facon  que 
les  pn>d nits  repn'senti nt,  unssi  upproximativement  que  possible,  la  de'pense 
ordinaire  d'nne  famille  ouvriere,  'In  type  observe',  qui  achl  le  <tn  detail  les 
obfets  ne'cessaires  a  Valirhentation  et  au  chauffage." — Vol.  IV,  pp.  252—253. 

1  I  think  T  am  aware  of  the  criticisms  that  may  be  urged  against 
the  assumption  that  th<-  varying  prix  de  pension  is  representative  of 
the  varying  standard  of  life.  My  study  is  intended  as  a  first  approxi- 
mation, and  T  hope  that  judgment  will  be  suspended  until  the  argu- 
ment of  the  chapter  is  completed. 

3  Ibid.,  Vol.  IV,  pp.  244-245,  l'57-258. 


30  Laws  of  Wages 

il  doit  arriver  et  il  arrive  en  effet  que  le  salaire  de 
Vouvrier  se  borne  a  ce  qui  lid  est  necessaire  pour  lui 
procurer  sa  subsistance."1 

If  this  doctrine  has  any  relevancy  to  the  conditions 
of  France  to-day,  one  would  say,  a  priori,  that  the 
wages  of  unskilled  laborers  must  be  in  close  associa- 
tion  with  the  cost  of  the  means  of  subsistence.  If 
the  relation  between  the  two  is  one  of  cause  and  effect, 
that  is  to  say,  if  the  wages  of  unskilled  laborers  are 
determined  by  the  means  of  subsistence,  then  the  de- 
gree of  association  must  approach  unity.  These  corol- 
laries of  the  Turgot  doctrine  may  be  tested  by  means 
of  columns  II  and  IV  of  Table  I. 

Turgot's  doctrine  relates  to  real  wages.  Column 
IV,  as  we  have  seen,  is  the  cost  in  the  different  de- 
partements  of  a  fixed  mode  of  life  that  approaches  the 
necessary  means  of  subsistence  of  a  laborer's  family. 
If  the  relation  between  means  of  subsistence  and 
the  wages  of  unskilled  laborers  is  a  relation  of  cause 
and  effect,  then  the  money  wages  of  unskilled  laborers 
in  the  several  departements  should  be  closely  correlated 
with  the  corresponding  prices  of  the  means  of  subsist- 
ence in  the  departements. 

How  close  is  the  association  actually  found  to  be  ? 
The  graph  showing  the  relation  between  the  variation 
in  the  cost  of  subsistence  and  the  wages  of  unskilled 
laborers  is  given  in  Figure  2.  The  law  of  the  asso- 
ciated variation  of  wages  with  the  cost  of  subsistence 
is  the  equation  to  the  straight  line,  namely,  ?/=  .864 

1  Turgot :  Reflexions  sur  la  formation  et  la  distribution  des  richesses. 


Means  of  Subsistence  and  the  Standard  of  Life     31 


«5 


(V  0>  (o  *) 

0)  <V  <\I  W 


32  Laws  of  Wages 

-f  .0014  x.  The  coefficient  of  correlation  is  r=.306. 
If  we  agree  to  regard  values  of  r  less  than  .25  as 
indicating  low  correlation;  between  .25  —  .50,  as 
fair  correlation;  .50  — .75,  as  high  correlation;  and 
.75  —  1.00,  as  very  high  correlation,  then,  we  may  say 
that  the  correlation  between  the  wages  of  unskilled 
laborers  and  the  means  of  subsistence,  as  tested  by 
the  official  data  for  France,  is  only  fair.  We  do  not 
overlook  the  facts  that  the  computation  of  column 
IV  presented  very  great  difficulties,  and  that  if  rent, 
properly  estimated,  had  been  included  and  the  re- 
maining figures  had  been  more  accurately  determined, 
a  closer  relation  might  have  been  discovered. 

The  hypothesis  of  the  causal  relation  between  the 
means  of  subsistence  and  the  wages  of  unskilled 
laborers  may  be  tested.  If  the  relation  between  the 
two  were  a  relation  of  cause  and  effect,  then  r  should 
approach  unity.1  It  is  found,  however,  that  the 
actual  value  of  r  is  .306 ±.066.  When  the  probable 
error  of  r  is  considered,  it  is  seen  that,  if  the  means 
of  subsistence  and   the  wages    of  unskilled  laborers 

CD        ■% 

were  in  causal  relation,  such  a  deviation  of  r  from 
unity  as  .306  would  be  practically  impossible. 

So  far  as  the  data  under  investigation  represent  the 
conditions  of  France  to-day,  it  may  be  said  — 

(1)  that  the  wages  of  unskilled  laborers  vary  in 
the  same  direction  as  the  cost  of  the  means 
of  subsistence  ; 

1  Pearson  :   Grammar  of  Science,  2d  edit.,  p.  397. 


Means  of  Subsistence  and  the  Standard  of  Life     33 

(2)  that  the  law  of  the  association  of  the  wages  of 

unskilled    laborers    and   the    means   of    sub- 
sistence is  lineal  ; 

(3)  that  the  value  of  the  coefficient  of  correlation 

is  r=. 306. ±.066. 

(4)  that  there  is  no  relation  of  cause  and   effect 

between  the  two. 

These  conclusions  are  based  upon  the  data  for  all 
of  the  87  dipartements  of  France,  excepting  the  Seine 
and  Rhin  (Ilaut).  For  the  latter,  no  record  is  avail- 
able in  case  of  column  IV.  The  Seine,  being  the 
departement  of  Paris,  presents  anomalous  conditions. 

Wages  and  the  Standard  of  Life. 

Despite  Lassalle's  intrepretation  of  Ricardo,  the 
classic  theory  of  the  relation  of  wages  to  the  standard 
of  life  is  found  in  Ricardo's  chapter,  "  On  Wages." 

"  The  natural  price  of  labour  .  .  .  depends  on  the  price  of 
the  food,  necessaries  and  conveniences  required  for  the  support 
of  the  labourer  and  his  family."  "  It  is  not  to  be  understood 
that  the  natural  price  of  labour,  estimated  even  in  food  and 
necessaries,  is  absolutely  constant.  It  varies  at  different  times 
in  the  same  country  and  very  materially  differs  in  different 
countries.*' 1 

The  thesis  is  that  the  standard  of  life  varies  in  time 
and  in  place  and  that  the  wages  of  laborers  vary 
pari  passu.  The  phases  of  the  doctrine  relating  to 
local  variations  will  be  subjected  to  a  test. 

1  Ricardo  :  Principles  of  Political  Economy  and  Taxation.  McCulloch's 
edition,  pp.  50,  52. 


3-4  Laws  of  Wages 

Do  the  wages  of  unskilled  laborers  in  France  vary 
with  the  local  variations  in  the  standard  of  life  ?  If 
a  concomitant  variation  does  exist,  what  is  the  meas- 
ure of  the  degree  of  association  between  the  variables  ? 
An  approximate  answer  to  these  questions  may  be  ob- 
tained from  the  data  of  Table  I.  In  column  II  of 
that  Table  are  recorded  the  average  wages  of  unskilled 
laborers  in  the  several  departements.  In  column  V,  the 
local  values  are  tabulated  of  our  representative  of  the 
standard  of  life  —  the  prix  ordinaire  de  pension  paye 
par  Vouvrier  isole  pour  le  logement  et  la  nourriture. 

From  these  data  we  find  — 

(1)  that  the  money  wages  of  unskilled  laborers  vary 

in  the  same  direction  as  the  cost  of  the  stand- 
ard of  life  ; 

(2)  that  the   law  of  the  association  of  the  money 

wages  of  unskilled  laborers  and  the  cost  of  the 
standard  of  life  is  linear  ; 

(3)  that  the  money  wages  of  unskilled  laborers  are 

much  more  closely  related  to  the  cost  of  the 
standard  of  life  than  to  the  cost  of  the  means 
of  subsistence.  In  the  former  case  r=  .667  ; 
in  the  latter,  r  —  .306. 

The  graph  representing  the  relation  of  the  two 
variables  is  given  in  Figure  3.  In  making  the  com- 
putations, all  of  the  departements  for  which  records  ex- 
ist were  considered  except  Gironde  and  Maine-et- 
Loire. 

Figure  3  exhibits  the  law  of  the  variation  of  wages 


Means  of  Subsistence  and  the  Standard  of  Life     35 


§  1 


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36  Laws  of  Wages 

of  unskilled  laborers  as  the prix  de  pension  varies  from 
departement  to  departement.  If  the  prix  de  pension 
were  taken  as  a  function  of  the  wages  of  unskilled 
laborers  we  should  have,  as  the  equation  of  the  rela- 
tion between  the  two  variables,  y  =  .5786  x+  .2537, 
Avhere  x  is  put  for  the  wages  of  unskilled  laborers. 
From  this  equation  it  is  clear  that,  for  an  increase 
of  one  franc  in  the  wages  of  unskilled  laborers, 
there  is  on  the  average  an  increase  of  about  58 
centimes  in  ike  ])rix  de  pension. 

There  is  a  subtle  difficulty  to  be  overcome  before 
our  investigation  can  be  brought  into  closer  relation 
with  the  Ricardian  doctrine.  The  preceding  results 
are  conclusions  as  to  the  relation  between  money 
wages  and  the  prix  de  pension.  But  the  Ricardian 
doctrine,  postulating  an  invariable  money  unit,  is  a 
theory  as  to  the  relation  of  wages  and  the  concrete 
things  composing  the  standard  of  life.  Would  it  be 
possible  to  close  the  gap  between  our  results  and  the 
Ricardian  theory  ? 

The  statistical  calculus  supplies  the  tool  for  connect- 
ing the  empirical  conclusions  with  the  a  priori  doctrine. 
Thus  far  it  has  been  shown  that  the  money  wages  of 
unskilled  laborers  are  correlated  with  the  prix  de 
pension  and  also  with  the  coefficient  de  depense  en  ob- 
jets  d' alimentation  et  de  chauffage.  Let  us  represent 
the  coefficient  measuring  the  correlation  in  the  first 
case  by  r„,  and  in  the  second  case  by  rls.  The  coeffi- 
cient de  depense,  we  know,  is  the  money  value  of  the 
same  kinds  and  quantities  oi  things  in  the  different  de- 

/ 


Means  of  Subsistence  and  the  Standard  of  Life     3*3 

partements,  wliile  the  prix  de  pension  is  the  price  of 
a  standard  that  varies  from  departi  ment  to  d&parti  ment. 
As  the  former  represents  the  variation  in  the  purchas- 
ing power  of  money  in  the  different  regions  of  France, 
we  should  infer  that  the  prix  de  pension  would  he 
correlated  with  the  coefficient  de  dipense.  Let  the 
measure  of  correlation  in  this  case  be  r.,.A.  In  order 
to  connect  our  results  with  the  Ricardian  theory  it  is 
necessary  to  eliminate  from  the  empirical  conclusion 
as  to  the  relation  of  the  money  wages  of  unskilled 
laborers  to  the  price  of  the  standard  of  life  the  factor 
due  to  the  local  variation  in  the  purchasing  power  of 
money. 

According  to  the  theory  of  the  partial  coefficient 
of  correlation,1  if  three  variables  are  so  interrelated 
that  their  gross  coefficients  of  association  are  respec- 
tively r12,  r13,  r23,  then  the  partial  or  net  coefficient  of 
correlation  between  the  variables  1  and  2  is  measured 

by  Pi>  =  -        '2       '*  2S  Using;   this    method   of 

treating  our  problem,  we  find  that  the  net  correla- 
tion between  the  wages  of  unskilled  laborers  and 
their  standard  of  life  is  pv2  =  .628,  where  the  r  sym- 
bols in  the  above  formula  for  pv2  have  the  meanings 
described  in  the  preceding  paragraph.  The  actual 
values  of  these  coefficients  are  r12=.6667  (the  coeffi- 
cient of  correlation  between  money  wages  of  un- 
skilled laborers  and  the  prix  de  pension)  ;  r13=  .306  1 

1    See  G.  Udny  Yule:  "On  The  Theory  of  Correlation."     Journal 
of  the  Royal  Statistical  Society,  December,  18U7. 


38  '  Laws  of  Wages 

(the  coefficient  of  correlation  between  the  money 
wages  of  unskilled  laborers  and  the  coefficient  de 
depense  en  objets  d 'alimentation  et  de  chauffage) ; 
r23=. 3405  (the  coefficient  of  correlation  between  the 
prix  de  pension  and  the  coefficient  de  depense  en  objets 
d' alimentation  et  de  chauffage).1 

From  this  result  it  follows  that,  so  far  as  the  data 
upon  which  the  investigation  rests  may  be  assumed 
to  be  representative  of  the  true  values  of  the  factors 
in  the  problem,  the  degree  of  association  between  the 
wages  of  unskilled  laborers  and  their  standard  of 
life'2  is  measured  by  pl2=  .628. 

1  In  computing  the  value  of  r23,  all  of  the  records  were  used  ex- 
cept that  for  Lozere. 

2  I  have  been  unable  to  find  in  the  French  report  any  precise  def- 
inition of  the  terra  Vouvrier  isole  as  it  appears  in  the  investigation 
concerning  prix  de  pension  paye'  par  Vouvrier  isole  pour  le  logement  et  la 
nourriture.  Does  it  refer  to  the  single  unskilled  laborer,  or  to  the 
single  skilled  laborer,  or  was  it  impossible  to  measure  the  difference 
between  the  prix  de  pension  of  the  two  classes  of  laborers?  The  last 
interpretation  would  seem  most  probable ;  for  the  attempt,  in  Vol.  IV, 
p.  260,  to  compare  the  wages  of  skilled  and  of  unskilled  laborers  with 
the  prix  de  pension  paye  par  Vouvrier  isole  assumes  a  common  prix  de 
pension  for  the  two  classes  of  laborers. 

It  may  be  noted  incidentally  that  the  present  chapter  contains  a 
solution  of  the  problem  that  is  abandoned  in  the  French  report. 
"A  vrai  dire,  la  relation  qui  pent  exister  entre  le  salaire  et  la  depense 
pour  le  logement  et  la  nourriture  nesemble  ni  directe,ni  simple."  —  p.  2G0. 
The  relation  is  both  direct  and  simple  and  the  coefficient  measuring 
the  degree  of  the  net  relation  is  p  =  .628. 

The  justness  of  taking  the  prix  de  pension  as  the  representative  of 
the  standard  of  life  of  unskilled  laborers  is  reenforced  by  the  consid- 
eration that  the  mean  value  of  the  prix  de  pension  d'un  ouvrier  isole  is 
76  per  cent  of  the  mean  value  of  the  wages  of  unskilled  laborers. 
It  therefore  represents  with  a  high  degree  of  accuracy  the  effort  of 
the  unskilled  laborer  to  maintain  a  standard  that  varies  from 
de'partement  to  departement. 


Means  of  Subsistence  and  the  Standard  of  Life     39 

Wages  of  Skilled  and  of  Unskilled  Laborers. 

Table  I  supplies  data  for  measuring  a  relation  that 
has  great  importance  for  the  theory  of  Chapter  IV, 
and  for  the  appreciation  of  practical  schemes  that 
have  for  their  aim  the  raising  of  the  level  of  general 
wages.  What  is  the  relation  between  the  variation 
in  the  wages  of  skilled  and  of  unskilled  laborers  ? 
The  results  that  are  about  to  be  given  are  based 
upon  a  consideration  of  all  of  the  87  dipartements 
of  France,  except  three,  —  Seine,  Seine- et-Mame, 
Seine-et-Oise,  which  are  unduly  affected  by  the  pecul- 
iar conditions  of  wage  receiving  in  Paris. 

We  find  — 

(1)  that  the  wages  of  skilled  and  of  unskilled  la- 

borers vary  in  the  same  direction  ; 

(2)  that  the  law  of  the  relation  is  linear ; 

(3)  that  the  coefficient  of  correlation   is  r  =  .775, 

which  is  higher  than  the  coefficient  measur- 
ing the  correlation  between  the  wages  of 
unskilled  laborers  and  the  cost  of  the  stand- 
ard  of  life. 

The  graph  representing  the  relation  is  given  in 
the  accompanying  Figure  4.  The  equation  to  the 
straight  line  is  y  =  1.24  -I-  .9142  x,  where  x  =  the  wages 
of  unskilled  laborers. 

Inasmuch  as  both  classes  of  wag;es  are  affected 
by  the  local  variations  in  the  purchasing  power  of 
money,  the  net  relation  between   the   two    variables 


40 


Laws  of  Wages 


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Means  of  Subsistence  and  the  Standard  of  Life     11 

can  be  found  only  after  the  money  factor  is  elimi- 
nated. If,  as  in  a  previous  case,  we  represent  the 
correlation  between  the  wages  of  skilled  laborers  and 
the  wages  of  unskilled  laborers  by  r12;  the  correla- 
tion between  the  wages  of  skilled  laborers  and  the 
coefficient  <le  depense  en  objets  d1  alimentation  et  de 
chauffage  by  r13;  and  the  correlation  between  the 
wages  of  unskilled  laborers  and  the  coefficient  de  de- 
pense by  r23 ;  then,  the  net  correlation  between  the 
wages  of  skilled  laborers  and  the  wages  of  unskilled 
laborers  is  pv2=  .757. 

We  have  now  definite  quantitative  solutions  to  the 
problems  we  set  out  to  examine.  The  wages  of  un- 
skilled  laborers  vary,  from  place  to  place  in  the  same 
country,  directly  (1)  with  the  cost  of  the  means  of 
subsistence,  (2)  with  the  standard  of  life,  the  close- 
ness of  the  relation  being  measured,  respectively, 
by  r=.o0(>,  p=.028.  The  wages  of  skilled  laborers 
vary  directly  with  the  wages  of  unskilled  laborers, 
the  degree  of  the  association  being  measured  by 
p  = .  7  o  7 . 

The  very  high  correlation  between  the  wages  of 
skilled  laborers  and  the  wages  of  unskilled  laborers 
suggests  the  wisdom  of  further  investigation  as  to 
the  mechanism  of  their  relation.  This  investigation 
is  supplied  in  Chapter  IV,  on  "  Wages  and  Ability." 


42 


Laws  of  Wages 


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CHAPTER   III 

WAGES   AND   THE   PRODUCTIVITY   OF   LABOR 

"  However  wages  may  be  adjusted  by  bargains  freely  made  by 
individual  men,  the  rates  of  pay  that  result  from  such  transactions 
tend  ...  to  equal  that  part  of  the  product  of  industry  which  is 
traceable  to  the  labor  itself." 

11  We  must  ascertain  whether  evolution  makes  labor  more  pro- 
ductive, and  therefore  better  paid,  or  less  productive  and  therefore 

worse  paid." 

—  John  Bates  Clakk. 

A  complete  theory  of  wages  faces  two  fundamental 
inquiries :  (1)  as  to  the  law  and  cause  of  the  varia- 
tion in  the  share  of  the  product  of  industry  consti- 
tuting general  wages ;  and  (2)  as  to  the  law  and 
cause  of  the  distribution  of  general  wages  among  the 
members  of  the  labor  group.  According  to  the  pro- 
ductivity theory  of  wages,  the  principle  of  the  specific 
productivity  of  labor  supplies  the  clew  to  the  satis- 
factory solution  of  both  inquiries.  It  is  the  purpose 
of  the  present  chapter  to  treat  statistically  certain 
phases  of  the  first  part  of  this  theory,  which  is  con- 
cerned with  the  determination  of  the  rate  of  general 
wages.  In  the  following  chapter  the  second  part 
will  receive  its  proper  attention. 

We  shall  approach  the  very  kernel  of  the  produc- 
tivity  theory  by  successive  stages.  Three  essential 
propositions   in   the  theory   will   be   established.     It 

44 


Wages  and  the  Productivity  of  Labor  r> 

will  be  demonstrated  first  that  in  a  particular  indus- 
try in  which  labor  plays  a  relatively  large  role  in 
production,  the  fluctuation  in  the  rate  of  general 
wages  varies  directly  with  the  fluctuation  in  the 
value  of  the  product  per  laborer.  It  will  then  be 
established  that  the  fluctuation  in  the  laborer's  rela- 
tive share  in  the  value  of  the  product  varies  directly 
with  the  fluctuation  in  the  amount  of  machine-power 
per  laborer  employed  in  the  industry.  In  the  third 
place,  a  proof  in  a  particular  instance  will  be  supplied 
of  an  important  dynamic  corollary  of  the  productivity 
theory  of  wages,  namely,  that,  other  conditions  re- 
maining the  same,  the  general  trend  of  the  laborer's 
share  of  the  product  is  determined  by  the  ratio  in 
which  capital  and  labor  are  combined  in  production. 
These  three  investigations  will  bring  to  a  statistical 
test  the  essential  propositions  in  the  productivity 
theory :  the  rate  of  general  wages  will  be  related 
to  the  productivity  of  labor,  and  the  secular  trend 
of  the  laborer's  share  in  distribution  will  be  brought 
into  functional  dependence  upon  the  ratios  in  which 
capital  and  labor  cooperate  in  production. 

Description  of  Data. 

The  data  forming  the  basis  of  the  investigation 
are  drawn  from  the  history  of  coal  mining  in  France. 
It  is  highly  desirable  that  all  three  of  the  proposi- 
tions which  have  just  been  described  should  be  in- 
vestigated with  reference  to  the  same  industry,  and 
it  is  necessary,  if   the  statistical   inductions  are  to 


t6  Laws  of  Wages 

have  value,  that  the  investigation  should  extend  over 
a  great  number  of  years.  These  desiderata  obviously 
impose  unusual  statistical  conditions  in  the  selection 
of  material ;  for  they  require  that  the  statistical 
record  shall  cover  many  items  that  are  difficult  to 
ascertain  and  shall,  in  addition,  be  relatively  uniform 
over  a  long  period  in  its  method  of  tabulation. 
There  is  only  one '  industry  in  France  for  which  the 
required  material  is  supplied,  and  I  am  not  aware  of 
the  existence  in  any  other  country  of  data  comparable 
in  fullness  of  detail  and  in  length  of  time  over  which 
the  record  is  available.  The  figures  upon  which  the 
investigation  rests,  and  which  appear  in  the  three 
tables  at  the  end  of  this  chapter,  have  been  taken 
from  the  careful  work  by  M.  Francois  Simiand2  on 
Le  Salaire  des  oavriers  des  mines  de  charbon  en  France. 

Fluctuations  in  the  Fate  of  Wages  and  in  the  Value 

of  the  Product. 

The  first  proposition  to  be  established  is  that,  in 
an  industry  in  which  labor  plays  the  leading  role  in 
production,  the  fluctuation  in  the  daily  rate  of  gen- 

1  "  La  seule  industrie  dont  en  France  on  connaisse  chaque  ann6e 
par  une  publication  officielle  le  nombre  des  ouvriers,  leur  salaire 
moyen  journalier  et  leur  gain  annuel,  la  production  et  le  prix  de 
vente,  est  celle  des  mines  de  houille." —  Levasseur :  Salariat  et  Salaires, 
p.  31. 

-  M.  Simiand  has  dealt  in  his  own  manner  with  the  first  proposi- 
tion developed  in  this  chapter.  His  acute  study  also  contains  a 
valuable  section  on  the  relation  of  the  use  of  machinery  to  the  rate 
of  wages.  I  am  greatly  indebted  to  M.  Simiand  for  the  data  that  I 
have  taken  from  his  masterly  treatise,  but  I  have  not  borrowed  from 
him  either  method  or  ideas. 


Wages  and  the  Productivity  of  Labor  47 

eral  wages  varies  directly  with  the  fluctuation  in  tke 
value  of  the  daily  product  per  laborer.  The  proposi- 
tion is  taken  in  this  form  simply  as  a  first  approxi- 
mation to  the  theoretical  principle  that  the  rate  of 
wages  varies  directly  with  the  marginal  productivity 
of  labor. 

It  is  quite  a  difficult  task  to  ascertain  directly  the 
statistical  equivalent  of  the  marginal  productivity  of 
labor,  and,  of  course,  no  record  exists  of  the  varia- 
tion of  the  marginal  productivity  throughout  a  term 
of  years.  Fortunately  for  the  inductive  proof  of 
this  important  principle,  it  is  not  necessary  to  treat 
the  theory  in  the  form  of  the  marginal  statement.  The 
way  out  of  the  difficulty  has  been  -supplied  by  the 
analysis  of  Professor  Clark. 

In  its  cruder  form,  as  it  wras  first  enunciated  in 
principle  by  Von  Thiinen,  the  marginal1  productivity 
theory  of  wages  implied  that  at  a  given  time  the 
marginal  laborer  —  wrho  for  the  sake  of  simplicity 
was  assumed  to  be  the  laborer  most  recently  set  at 
work  —  produced  less  than  the  laborers  who  were 
employed  earlier,  and  that  the  advent  of  the  mar- 
ginal man  not  only  reduced  the  amount  that  could  be 
claimed  by  all  the  laborers,  but  was  the  occasion  for 
diverting  a  part  of  the  product  of  the  earlier  laborers 
to  capitalists  and  entrepreneurs.  It  wras  one  of  the 
many  services  of  Professor  Clark  to  show  that  the  spe- 
cific product  of  every  unit    of  labor  is  equal  to  the 

1  It  is  not  meant  to  suggest  that  Von  Thiinen  used  the  words 
''marginal  productivity." 


In  Laws  of  Wages 

product  of  the  marginal  unit,  that,  at  any  given  time, 
all  units  are  alike  in  their  productivity,  that  the  fall 
in  the  productivity  of  labor  occasioned  by  the  advent 
of  a  new  worker  is  due  to  a  reapportionment  of  capi- 
tal which  gives  to  each  laborer  a  smaller  amount  of 
capital  as  cooperating  adjunct,  and  that  the  produc- 
tivity of  general  labor  is  equal  to  the  sum  of  the  pro- 
ductivity of  its  constituent  items.  In  view  of  this 
analysis,  it  follows  that  if  an  industry  could  be  dis- 
covered in  which  labor  played  the  chief  role  in  pro- 
duction, the  variations  in  the  mean  value  of  the 
product  per  laborer  per  day  would  be  a  close  first 
approximation  to  the  variations  in  the  specific  pro- 
ductivity of  labor. 

Table  I,  in  the  Appendix  to  this  chapter,  has  been 
compiled  as  follows :  Column  II,  giving  the  mean 
daily  rate  of  wages,  is  derived  from  two  items,  (1) 
the  total  amount  paid  annually  in  wages,  and  (2) 
the  number  of  days'  work  during  the  year.  This 
second  item  is  equal  to  the  sum  of  the  products  of 
the  number  of  laborers  employed  for  various  intervals 
of  the  year  by  the  number  of  days  during  which  they 
were  respectively  employed.  Item  (1)  divided  by 
item  (2)  gives  the  mean  daily  rate  of  wages  tabu- 
lated in  column  II.1  Column  III  is  likewise  derived 
from  two  items,  (1)  the  value  of  the  total  annual  prod- 
uct at  the  place  of  production,  (2)  the  number  of 
days'  work  during  the  year.     The  second  item  is  the 

1  Simiand  :  Le  Salaire  des  ouvriers  des  mines  de  charbon  en  France, 
pp.  24-25. 


Wages  and  the  Productivity  of  Labor  40 

same  as  the  second  item  in  the  preceding  case.  The 
figures  tabulated  in  column  III,  giving  the  mean 
value  of  the  daily  product  per  laborer,  are  the  ratios, 
for  successive  years,  of  the  value  of  the  annual  prod- 
uct divided  by  the  aggregate  number  of  days'  work 
per  year.1  Columns  II  and  III,  which  record  the 
simultaneous  variations  of  the  two  factors  for  a 
period  of  fifty-six  years,  afford  an  ample  basis  for 
investigating  the  relation  between  the  mean  daily  rate 
of  wages  and  the  mean  value  of  the  daily  product  per 
laborer.  It  should  be  remembered  that,  in  case  of  the 
French  coal  miners,  no  formal  sliding  scale  system 
by  which  wages  varied  with  the  value  of  the  product 
existed  during  the  period  covered  by  this  study.2 

On  Figure  5  is  traced,  for  a  period  of  fifty-six  years, 
the  history  of  the  variation  of  the  mean  daily  wages 
and  of  the  mean  value  of  the  daily  product  per 
laborer.  In  each  case  the  history  of  the  change  is 
recorded  in  an  ascending;  ziy:za<>;  line,  which  is  the  re- 
sultant  of  the  forces  determining  its  mean  direction 
and  the  forces  producing  the  vicissitudes  portrayed  in 
the  fluctuations  about  the  line  of  general  trend.  The 
proposition  with  which  we  are  at  present  concerned  is 
that,  at  a  given  time,  the  variation  in  the  productiv- 

1Simiand:  Le  Salaire  des  ouvrierx  </«  mines  de  charbon  en  France, 
p.  98. 

2"Sans  doute,  nous  savons  qu'en  fait  1<-  systeme  *  1 1 1  de  I'echelle  mo- 
bile, qui  fait  varier  le  salaire  suivant  une  certaine  relation,  en  raison 
(It's  variations  du  prix  du  produit  dans  le  sens  de  la  baissc  aussi  luen 
que  dans  le  sens  de  la  hausse,  n'a  jamais  (•{>'•  adopte*  par  les  ouvriera  el 
patrons  francais."  —  Simiand  :  Le  Salaire,  etc.,  |>.  227.  Cf.  also  pp. 
195-196,  19G  u. 


50 


Laws  of  Wages 


Wages  and  the  Productivity  of  Labor  ~>\ 

ity  of  labor  is  accompanied  with  a  variation  of  wages 
in  the  same  direction.  That  is  to  say,  as  an  average 
result,  an  increase  or  decrease  in  the  productivity  of 
labor  is  accompanied  with  an  increase  or  decrease  in 
wages.  This  proposition,  therefore,  is  a  thesis  ail'ect- 
ing  the  fluctuations  about  the  general  trend,  and  con- 
sequently, in  order  to  bring  the  two  series  to  a 
comparable  basis,  their  differences  due  to  their  differ- 
ence in  general  trend  must  be  eliminated.  Our  first 
problem,  then,  is  to  find  the  equation  to  the  general 
trend  of  the  figures  in  each  series. 

If  the  type  of  equation  for  each  series  be  taken  as 
of  the  geometric  order  y  =  ABr,  and  the  constants 
A,  B  be  evaluated  by  the  method  of  moments,  the 
equation  to  the  general  trend  for  the  wage  series  is 
//=  2.1063(1.015)<B,  and,  for  the  series  of  the  values  of 
the  product,  y=  5. 1115(1. 012)3",  the  origin,  in  both 
cases,  being  at  1847.  The  two  equations  are  repre- 
sented upon  Figure  5  by  the  smooth  curves  passing 
through  the  two  series  of  numbers. 

The  knowledge  of  the  equations  to  the  curves  of 
general  trend  makes  possible  the  next  step  in  the 
problem,  which  is  the  computation  of  the  relative 
deviations  of  the  actual  figures  from  the  g-eneral  trend. 
The  actual  figures,  as  we  know,  are  recorded  by  the 
zigzag  line.  The  absolute  deviations  of  the  actual 
figures  for  the  successive  years  are  obtained  by  sub- 
tracting from  the  actual  figure  for  each  year  the 
value  of  the  general  trend  for  the  same  date.  For 
example,  the  absolute  deviation  for  1900,  in  case  of 


52 


Laws  of  Wages 


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Wages  and  the  Productivity  of  Labor  53 

the  daily  product,  was  10.78-9.43=1.35,  because 
the  mean  value  of  the  daily  product  per  laborer,  in 
1900,  was  10.78  francs,  and  the  value  of  the  general 
trend  for  the  same  year  was  y=  5.1115  (1.0 J  2;  ;  = 
9.43  francs.  The  relative  deviation  of  the  actual 
figures  for  each  vear  is  the  ratio  of  the  absolute  devi- 
ation  to  the  corresponding  value  of  the  general  trend. 

-|     q  - 

In  1900,  the  relative  deviation  was  -1—  =  14.3  per 

J  .4:0 

cent,  It  is  desirable  to  deal  with  the  relative,  in- 
stead of  the  absolute,  deviations  because  the  two 
series  of  figures  move  about  axes  with  different 
absolute  values  and  with  different  rates  of  change. 

After  the  relative  deviations  of  the  two  series  of 
figures  have  been  computed,  it  is  possible  to  treat 
their  correlation.  On  Figure  G  the  relative  devia- 
tions of  the  two  series  are  plotted  about  a  horizontal 
line.  It  is  quite  evident  from  the  general  concurrent 
flow  of  the  curves  that  the  two  series  of  percentage 
deviations  are  closely  associated.  What  is  the  meas- 
ure of  the  degree  of  their  correlation  ? 

The  computation  of  the  coefficient  of  correlation 
by  the  usual  method  gives  r  =  .843.  ligure  7 
shows  the  regression  of  the  percentage  deviation 
in  the  mean  daily  wage  upon  the  percentage  devi- 
ation in  the  mean  value  of  the  daily  product  per 
laborer. 

We  conclude,  therefore,  from  this  part  of  the  in- 
vestigation, that,  in  case  of  the  great  industry  of  coal 
mining  in  France,  — ■ 


54 


Laws  of  Wages 


s-aSeM  /f//epueau/  a/  suou&Aap  aSp/ua^u^ 


<*•     t)     <o 
■       i       t 


Wages  and  the  Productivity  of  Labor  55 

(1)  the  fluctuation  in  the  mean  daily  rate  of  wages 

varies  directly  with  the  iluctuation  in  the 
mean  value  of  the  daily  product  of  the 
laborer ; 

(2)  the  coefficient  measuring  the  degree  of  associa- 

tion between  the  percentage  variation  in  the 
rate  of  wages  and  the  percentage  variation  in 
the  mean  value  of  the  daily  product  per  laborer 
has  the  very  high  value  of  r  =  .843. 

Fluctuations  in  the  Laborer  s  Relative  Share  of  the 
Product  and  in  the  Ratio  of  Capital  to  Labor. 

The  second  essential  proposition  in  the  productivity 
theory  of  wages  is  that  the  fluctuation  in  the  laborer's 
relative  share  in  the  value  of  the  product  varies  di- 
rectly with  the  fluctuation  in  the  amount  of  machine 
power  per  laborer  employed  in  the  industry.  The 
establishment  of  this  proposition  in  a  rigid  form 
would  give  to  the  productivity  theory  in  its  most 
important  aspect  the  sanction  of  inductive  proof. 
For  the  pure  theory  of  the  distribution  of  income  is 
a  theory  as  to  the  apportionment  of  the  product  of 
industry  between  the  agents  cooperating  in  its  pro- 
duction and  is,  therefore,  concerned  with  relative 
shares  of  the  product  and  not  with  their  absolute 
magnitudes.  Our  first  proposition  concerning  the 
relation  of  wages  to  the  value  of  the  product  is  a 
proposition  affecting  the  absolute  value  of  wages  and 
not  the  laborer's  relative  share  of  the  product  of  in- 
dustry.    The  proposition   that  we   are  about  to  ex- 


56  Laws  of  Wages 

amine  is  concerned  with  the  latter,  more  fundamental 
aspect  of  the  wages  question. 

Table  II  in  the  Appendix  exhibits  the  material 
upon  which  the  investigation  rests.  Column  II  of 
that  table  gives,  throughout  a  period  of  53  years,  the 
ratio  of  a  day's  wages  to  the  value  of  a  day's  product 
per  laborer.  The  two  items  from  which  the  ratios 
are  derived  may  be  obtained  from  Table  I.  Column 
III,  which  gives  the  amount  of  machine-power  per 
100  laborers  employed  in  mining,  is  derived  from  two 
items  that  are  taken  from  M.  Simiand's  work  ' : 
(1)  the  total  horse-power  of  the  machinery  employed 
in  the  mines,  and  (2)  the  number  of  laborers  so  em- 
ployed. The  figures  in  column  III  are  the  ratios  of 
these  two  items  expressed  as  the  number  of  horse- 
power per  100  laborers.  The  problem  that  will 
be  investigated  is  the  relation  of  the  variations 
of  the  figures  in  column  II  to  the  variations  in 
column  III. 

It  would  have  been  desirable  to  investigate  directly 
the  relation  of  the  variation  of  the  laborer's  share  of 
the  product  to  the  variation  of  the  amount  of  capital 
associated  with  labor  in  production.  But  the  figures 
for  the  capital  employed,  at  successive  years,  were 
not  accessible  to  me.  The  proposition  in  the  form  in 
which  it  will  be  tested  is  of  first  importance  in  itself, 
and  if  it  is  permitted  to  make  the  reasonable  assumption 
that  the  machine-power  employed  in  mines  is  directly 
related  to  the  amount  of  capital  employed,  then  the 

1  Simiand  :  Le  Salaire,  p.  49. 


Wages  and  the  Productivity  of  Labor  57 

establishment  of  the  proposition  in  its  present  form 
renders  practically  certain  the  doctrine  of  pure  eco- 
nomics that  the  laborer's  relative  share  of  the  product 
varies  directly  with  the  relative  amount  of  capital 
with  which  he  works. 

A  moment  ago  reference  was  made  to  the  exploita- 
tive implication  in  Von  Thiinen's  treatment  of  the 
productivity  principle.  To  affirm  that  the  marginal 
product  of  labor  decreases  with  an  increase  in  the 
labor  force  and  that  the  general  rate  of  wages  falls 
with  the  decrease  of  the  marginal  product,  leaves 
room  for  the  inference  that  the  earlier  laborers  are 
exploited  of  a  part  of  their  product  when,  in  conse- 
quence of  the  growth  of  the  labor  force,  the  marginal 
product  of  labor  decreases.  Professor  Clark,  as  we 
know,  has  shown  why  such  an  inference  is  unwar- 
ranted. The  explanatory  facts  are  that  the  increase 
of  the  labor  force  implies  a  reduction  in  the  average 
amount  of  capital  with  which  the  laborer  works,  and 
that  the  fall  of  the  general  rate  of  wages  is  due  to  a 
lessened  specific  productivity  of  labor  following  the 
per  capita  reduction  of  the  amount  of  capital  employed. 
Has  this  theory  relevancy  only  to  the  hypothetical 
static  state  that  forms  the  groundwork  of  theoretical 
speculation,  or  does  it  have  a  bearing  upon  the  highly 
dynamic  conditions  of  actual  industry  ?  The  investi- 
gation that  we  are  about  to  enter  upon  will  answer 
the  question. 

Our  present  query  has  this  form  :  Does  the  fluctua- 
tion in  the  laborer's  relative  share  of  the  product  of 


58 


Laws  of  Wages 


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Wages  and  the  Productivity  of  Labor  59 

industry  vary  directly  with  the  fluctuation  in  the 
relative  amount  of  machine-power  with  which  he 
works,  and  if  so,  how  closely  arc  the  concomitant 
variations  related  ? 

The  method  of  investigation  is  the  same  as  the  one 
wc  have  already  employed.  If  the  quantities  in  col- 
umns II  and  III  of  Table  II  are  plotted,  the  graphs  will 
take  a  generally  ascending  zigzag  course.  The  equa- 
tion to  the  general  trend,  in  case  of  the  ratio  of  wages 
to  the  value  of  the  product,  is  y  =  40.750(1. 0039)% 
and,  in  case  of  the  ratio  of  machine-power  to  men, 
y  =  28.758(1.025)"',  the  origin  in  both  cases  being 
IS 47.  On  Figure  8  the  percentage  deviations  are 
traced  about  a  horizontal  line,  and  on  Figure  9  the 
regression  of  the  percentage  deviation  of  the  first 
series  upon  the  percentage  deviation  of  the  second 
series  is  shown,  that  is  to  say,  the  regression  of  the 
percentage  deviations,  in  case  of  the  ratio  of  wages 
to  the  value  of  the  product,  upon  the  percentage 
deviations  in  case  of  the  ratio  of  machine-power  to 
men.     The  coefficient  of  correlation  is  r=  .599. 

We  conclude,  so  far  as  the  industry  of  coal  mining 
in  France  is  concerned, — 

(1)  that   the   fluctuation  in  the  laborer's    relative 

share  of  the  product  of  industry  varies  directly 
with  the  fluctuation  in  the  relative  amount 
of  machine-power  with  which  he  works ; 

(2)  that  the  coefficient  of  correlation    is  r=  .599. 

(3)  that   if  it   is   permitted   to    assume    that    the 


GO 


Laws  of  Wages 


a  value  of  the  da 
undred  laborers. 

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Wages  and  the  Productivity  of  Labor  61 

amount  of  machine-power  varies  directly  wit  h 
the  amount  of  capital  employed,  fcheo  the 
fluctuation  in  the  laborer's  relative  share  of 
the  product  of  industry  varies  directly  with 
the  fluctuation  in  the  relative  amount  of 
capital  employed. 


Tlie  General  Trend  of  Wages. 

The  third  essential  proposition  in  the  productivity 
theory  of  wages  is  that,  other  conditions  remaining 
the  same,  the  general  trend  of  the  laborer's  relative 
share  of  the  product  is  dependent  upon  the  ratio  in 
which  capital  and  labor  are  combined  in  production. 
Up  to  this  point  we  have  been  concerned  with  fluctua- 
tions about  the  general  trend  of  wages  ;  we  now  enter 
upon  the  question  of  the  general  trend  itself.  This 
corollary  of  the  productivity  theory  is  a  proposition 
in  dynamic  economics  ;  it  concerns  the  reward  of  the 
laborer  in  a  society  in  which  conditions  and  methods 
of  production  are  changing,  and  consequently  it  has 
a  very  direct  bearing  upon  concrete  industry. 

Because  of  the  lack  of  data  to  treat  this  proposition 
fully,  we  shall  be  compelled  to  approach  the  problem 
by  investigating,  in  a  particular  instance,  a  corollary 
of  the  proposition  before  us.  We  observe,  then,  that 
if  it  be  true  that  the  general  trend  of  the  laborer's 
relative  share  of  the  product  of  industry  increases 
witli  the  relative  amount  of  capital  with  which  he 
works,  it  would  follow  that,  in  the  same  industry,  in 


62  Laws  of  Wages 

neighboring  places,  with  similar  methods  of  produc- 
tion, the  general  trend  of  the  laborer's  share  would 
increase  most  rapidly  where  the  general  trend  of  the 
relative  amount  of  capital  per  laborer  employed  in- 
creased most  rapidly.  Or,  to  put  the  corollary  in  a 
form  in  which  it  will  admit  of  treatment  by  means 
of  available  statistics,  we  may  say  that  in  case  of 
the  same  industry,  in  neighboring  places,  other  con- 
ditions remaining  the  same,  the  general  trend  of  the 
laborer's  relative  share  of  the  product  will  increase 
most  rapidly  where  the  general  trend  of  machine 
power  per  laborer  increases  most  rapidly. 

Table  III  in  the  Appendix  exhibits  the  data  used 
in  the  investigation.  Column  II  gives  the  ratio,  per 
hundred  laborers,  of  the  machine-power  employed  in 
the  direct  exploitation  of  the  coal  mines  in  the  Bassin 
de  Nord.  Column  III  gives,  for  the  same  basin  and 
the  same  period,  the  ratio  of  daily  wages  per  laborer 
to  the  value  of  the  daily  product  per  laborer.  Columns 
IV  and  V  give  the  corresponding  data  for  the  neigh- 
boring Bassin  de  Pas-de- Calais.  All  of  the  figures 
have  been  taken  from  M.  Simiand's  work.1  The 
record  for  the  period  1880-1902  is  used  because  the 
figures  for  the  years  before  1880  are  not  comparable 
with  those  for  the  later  period.  M.  Simiand  gives 
figures  for  only  three  basins  -  -  Loire,  Nord,  and  Pas- 
de-Calais.  The  methods  of  exploitation  and  the  gen- 
eral conditions  of  production  in  case  of  the  neighboring 
basins  Nord  and  Pas-de-Calais  are  regarded  by  M. 

1  Simiand:  Le  Salaire,  p.  112. 


Wages  and  the  Product i rHy  <>f  Labor  03 

Simiand  as  being  so  much  alike  as  to  justify  his  class- 
ing them  together '  and  treating  them  in  sharp  con- 
trast to  the  southerly  Bassin  de  Loire. 

It  is  quite  clear,  therefore,  that  the  Bassin  de  Noril , 
and  the  Bassin  de  Pas-de- Calais,  because  of  their  be- 
ing in  neighboring  departements,  because  of  the  simi- 
lar methods  of  exploitation  and  the  similar  general 
conditions  of  production,  and  because  of  the  exist- 
ence of  statistical  material  covering  a  long  period, 
offer  a  favorable  case  for  testing  the  corollary  that 
has  just  been  formulated. 

Our  immediate  problem  is  to  find,  for  the  two  coal 
basins,  the  general  trend  of  the  increase,  first  of  the 
ratio  of  the  machine-power  per  hundred  laborers,  and 
secondly,  of  the  ratio  of  wages  to  the  value  of  the 
product.  In  case  of  the  data  as  to  the  ratio  of 
machine-power  to  the  number  of  men,  we  find,  by  us- 
ing the  same  method  that  has  already  been  employed 
in  this  chapter,  that  the  equation  to  the  general  trend 
for  the  Bassin  de  Nord  is  y=  46.815(1.0504)*,  and 
for  the  Bassin  de  Pas-de- Calais,  y  =  61. 793(1. 0344)*, 
the  origin  in  both  cases  being  at  1880.     As  both  of 

1  Simiand  :  Le  Salaire,  pp.  110-111.  "  II  suffit  a  uotre  dessein  de 
consid^rer  les  bassins  dont  l'importance  doniine  et  regie  Involution 
globale  tt  d'atteindre  les  cas  devolution  econonrique  les  plus  diver- 
gents  que  nous  puissious  rencontrer.  Or,  il  se  trouve  qu'a  tous  les 
moments  de  notre  experience,  Loire,  Nord  et  Pas-de-Calais  fournissent 
a  eux  seals  la  plus  grosse  part  de  la  production  francaise  totale  (d'abord 
sensiblement  plus  de  la  moiti£,  ensuite  jusqu'a  70%  el  plus).  Puis  une 
etude  anterieure  nous  a  hulique  que  le  bassin  de  la  Loire  d'une  part. 
Irs  liassins  du  Nord  et  du  Pas-de-Calais  de  l'autre, semblaient  s'opposer 
le  plus  nettement  au  point  tie  vue  de  la  conduite  gconomique." 


64 


Laws  of  Wages 


Wages  and  the  Productivity  of  Labor  65 

these  equations  are  of  the  geometric  form,  it  follows 
that  the  ratio  of  annual  increase  in  the  ratio  of 
machine-power  per  hundred  men,  for  the  Bassin  de 
Nord  is  1.0504,  and  for  the  Bassin  de  Pas-de-Calais 
is  1.0344.  II i -uce,  as  the  Bassin  de  Nord  offers  the 
greater  ratio  of  increase,  we  should  expect  to  find, 
according  to  the  principle  of  the  productivity  theory, 
that  the  ratio  of  the  laborer's  relative  share  in  the 
product  increased  more  rapidly  in  the  Bassin  de  Nord 
than  in  the  Bassin  de  Pas-de- Calais.  Before  passing 
to  the  question  of  wages,  we  should  note  that,  if  the 
equations  to  the  general  trend  for  the  relative  machine 
power  in  the  two  cases  be  put  in  the  form,  respec- 
tively, of  y=  100(1.0504)%  and  y=  100(1.0344)",  the 
upper  part  of  Figure  10  will  represent  the  relative 
ratios  of  increase  for  the  two  basins. 

In  case  of  the  data  as  to  the  ratio  of  wages  to  the 
value  of  the  product,  we  find  that  the  equation  to 
the  general  trend  for  the  Bassin  de  Nord  is 
y  —  49.139(1.0035)°',  and  for  the  Bassin  de  Pas-de- 
Calais,  y  =  44.697  (1.0013)'',  the  origin  in  both  cases 
being  at  1880.  The  ratio  of  the  annual  increase  in 
the  former  case  is  1.0035  and  in  the  latter  case  it  is 
1.0013.  If  the  two  equations  be  put  in  the  form  of 
//=  100  (1.0035)"- and  y  =  100  (1.0013)',  respectively, 
the  lower  part  of  Figure  10  will  represent,  for  the  two 
basins,  the  ratios  of  increase  of  the  laborer's  relative 
share  of  the  product.1 

1  In  order  to  make  visible  the  ratios  of  growth  in  the  two  cases,  the 
upper  and  the  lower  parts  of  Figure  10  arc  drawn  to  different  perpen- 
dicular scales. 


66  Laws  of  Wages 

We  find,  accordingly,  that,  true  to  the  principle  of 
the  productivity  theory, — 

(1)  the  general  trend  of  the  laborer's  share  of  the 

product  is  upward  where  the  general  trend  of 
machine-power  per  laborer  is  upward  ; 

(2)  the  ratio  of  increase  in  the    general  trend  of 

wages  is  greater,  the  greater  the  ratio  of  in- 
crease in  the  relative  amount  of  machine- 
power  with  which  the  laborer  works. 

If  it  is  reasonable  to  assume  that  the  amount  of 
machine-power  employed  in  coal  mining  varies  directly 
with  the  amount  of  capital  employed,  the  preceding 
investigation  justifies  the  conclusion  that  the  increase 
in  the  general  trend  of  the  laborer's  share  of  the  prod- 
net  is  greater,  the  greater  the  increase  in  the  general 
trend  of  the  ratio  of  capital  to  labor  employed  in  pro- 
duction. 

The  conclusions  of  this  chapter  have,  for  the  most 
part,  been  expressed  in  general  form,  while  the  ma- 
terial upon  which  the  investigation  rests  has  been 
drawn  from  the  history  of  one  industry  in  one  country. 
This  has  been  done  with  no  intention  of  exaggerating 
the  scope  of  the  inductive  inferences  nor  in  ignorance 
of  the  narrow  statistical  basis  upon  which  the  last 
proposition  rests.  The  purpose  of  the  investigation 
was  to  make  the  connection  between  certain  general 
conclusions  of  pure  economics  and  the  concrete  facts 
of  some  one  great  industry.     The  general  character  of 


Waycs  and  the  Productivity  of  Labor  67 

the  propositions  is  due  to  their  a  priori  origin  ;  the 
investigation  has  established  that,  far  from  being 
without  relevancy  to  actual  industry,  these  general 
propositions  are  the  accurate  description  of  the  eco- 
nomic laws  of  wages  in  the  one  great  industry  that 
has  been  subjected  to  inductive  treatment. 


68 


Laws  of  Wages 


APPENDIX 

TABLE  I. —  Daily  Wages  and  Mean  Value  of  Daily  Product 

per  Laborer 


Mean  Value 

Mean  Value 

Year 

Mean  Daily 
Wages 

of  the 

Daily  Product 

per  Laborer 

Year 

Mean  Daily 
Wages 

of  the 

Daily  Product 

per  Laborer 

I 

II 

III 

I 

II 

III 

1847 

2.07 

5.13 

1875 

3.58 

8.41 

1818 

2.14 

4.76 

1876 



1849 

2.16 

5.09 

1877 

^__^^_ 

1850 

2.14 

5.27 

1878 



1851 

2.07 

4.75 

1879 

1852 

2.04 

4.81 

1880 



1853 

2.20 

5.32 

1881 

1854 

2.32 

5.40 

1882 

3.71 

7.91 

1855 

2.35 

5.95 

1883 

3.84 

8.06 

l85i ; 

2.51 

6.32 

1884 

3.83 

8.06 

1857 

2.48 

5.93 

1885 

3.72 

8.05 

1858 

2.55 

5.97 

1886 

3.71 

7.71 

1859 

1887 

3.72 

7.65 

1860 

2.50 

5.73 

1888 

3.71 

7.60 

1861 

2.57 

5.94 

1889 

3.87 

7.88 

1862 

2.52 

5.89 

1890 

4.16 

8.84 

186:; 

2.69 

5.83 

1891 

4.17 

9.09 

1861 

2.60 

5.69 

1892 

4.24 

8.46 

1865 

2.69 

6.02 

1893 

4.14 

8.03 

1866 

2.76 

6.31 

1894 

4.14 

8.01 

]  867 

2.89 

6.52 

1895 

4.10 

7.!*:; 

1868 

•J.ur, 

6.45 

1896 

4.10 

7.86 

1869 

2.99 

6.58 

1897 

4.14 

8.08 

1870 

3.04 

6.55 

1898 

4.23 

8.41 

1871 

3.08 

6.88 

1899 

4.38 

9.21 

187  2 

3.:;5 

7.91 

1900 

4.66 

10.78 

1  ^7:5 

3.15 

9.30 

1901 

4.82 

10.68 

1874 

3.56 

8.93 

1902 

4.57 

9.75 

Wages  and  the  Productivity  of  Labor 


69 


TABLE  II.  —  Ratio  of  Daily  Wages  to  the  Value  of  a  Day's 
Product  per  Laborer  and  Ratio  of  Machine-Power  to 
One  Hundred  Laborers 


Ratio  of 

Ratio  of 

Daily  Wages 

Ratio  of 

Daily  Wages 

Ratio  of 

Year 

to  the  Value 

Machine-Power 

Year 

to  the  Value 

Machine-Power 

of  a  Day's 

to  100 

of  a  Day's 

to  100 

Product  per 

Laborers 

Product  per 

Laborers 

Laborer 

Laborer 

I 

II 

III 

I 

II 

III 

1847 

Kl.l 

32 

1874 

39.9 

43 

18  is 

45.0 

37 

1875 

42.6 

45 

1849 

42.5 

36 

1876 

43.1 

51 

1850 

40.7 

34 

1877 

45.0 

54 

1851 

43.6 

36 

1878 

45.5 

59 

1852 

42.5 

36 

1879 

15.7 

61 

185:; 

41.4 

32 

1880 

45.2 

61 

185  1 

13.0 

34 

1881 

45.6 

65 

1855 

30.5 

34 

1882 

46.9 

68 

1856 

39.7 

36 

1883 

17.7 

67 

1857 

41.8 

39 

1884 

47.5 

72 

1858 

42.7 

44 

1885 

46.2 

77 

1859 

— 

1886 

48.1 

82 

1 860 

43.7 

44 

1887 

48.6 

81 

1801 

43.3 

42 

1888 

48.8 

82 

1862 

42.8 

41 

1889 

49.1 

79 

1863 

46.2 

39 

1890 

47.0 

85 

186-4 

45.7 

38 

1891 

45.8 

87 

1865 

44.7 

40 

1892 

50.2 

92 

1866 

43.8 

44 

1893 

51.7 

100 

1867 

14.3 

44 

L894 

51.7 

108 

1868 

15.9 

45 

1895 

51.7 

105 

1869 

45.5 

47 

1896 

52.1 

108 

1870 

46.4 

49 

1897 

51.3 

111 

1S71 

44.8 

48 

1898 

50.3 

111 

187i' 

42.3 

44 

1S99 

47.6 

110 

1873 

37.1 

41 

70 


Laws  of  Wages 


TABLE  III.  —  Ratio  of  Machine-Power  to  One  Hundred 
Laborers  and  Ratio  ok  Daily  Wages  to  the  Value  of  a 
Day's   Product   per   Laborer 


Bassin  de  Nord 

Bassin  de 

Pas-de-Calais 

Ratio  of 

Ratio  of  Daily 

Ratio  of 

Ratio  of  Daily 

Year 

Machine-Power 
to 

Wages  to  the 
Value  of  a  Dav's 

Machine-Power 

to 

Wages  to  the 
Value  of  a  Day's 

100  Laborers 

Product  per  Laborer 

100  Laborers 

Product  per  Laborer 

I 

II 

III 

IV 

V 

1880 

45 

48.7 

64 

40.2 

1881 

46 

49.3 

63 

42.3 

1882 

48 

49.0 

71 

45.0 

1883 

50 

49.9 

72 

45.2 

1884 

58 

51.5 

70 

45.7 

1885 

68 

50.1 

70 

44.1 

1886 

69 

50.6 

85 

45.8 

1887 

71 

49.9 

82 

46.6 

1888 

77 

49.9 

83 

46.5 

1889 

77 

48.8 

79 

47.4 

1890 

82 

47.4 

75 

44.3 

1891 

79 

45.5 

78 

40.9 

1892 

85 

50.0 

83 

47.5 

1893 

90 

54.8 

94 

49.5 

1894 

91 

56.7 

115 

48.4 

1895 

90 

57.9 

104 

49.0 

1896 

95 

56.8 

101 

49.8 

1897 

93 

55.3 

110 

49.2 

1898 

92 

53.7 

109 

49.0 

1899 

107 

51.6 

97 

44.5 

1900 

137 

45.8 

125 

39.8 

1901 

153 

50.5 

149 

42.2 

1902 

156 

52.7 

146 

42.1 

CHAPTER   IV 
WAGES   AXI)   ABILITY 

"Le  capital i sine  .  .  .  tend  a  prod n ire  une  eertaine  realisation  du 
travail  entre  les  diverses  parties  de  I'usine;  mais  comme  il  a  besoin 
d"un  nombre  considerable  d'hommes  particulierement  actifs,  attentifs 
ou  experiment's,  il  s'ing6nie  a  donner  des  supplements  de  salaire  aux 
homines  qui  lui  rendent  ainsi  plus  de  services;  ce  n'est  point  par 
des  considerations  de  justice  qu'il  se  regie  dans  ce  calcul,  mais  par 
la  settle  recherche  empirique  d'un  equilil>re  regie  par  les  prix.  Le 
capitalisme  arrive  done  a  resoudre  tin  probleme  qui  semblait  insolu- 
ble, tant  qu'il  avait  et<-  rlud'n-  par  les  utopistes;  il  r6sou1  la  ques- 
tion de  r.-galit.'-  des  travailleurs,  tout  en  tenant  compte  des  inegalites 
naturelles  on  acquises  qui  se  traduisent  par  des  inegalites  dans  le 

travail." 

—  Georges  Sorel. 

In  the  preceding  chapter  we  examined  statistically 
the  most  important  aspects  of  the  first  of  the  two  in- 
quiries that  are  faced  in  a  complete  theory  of  wages, 
namely,  the  question  as  to  the  law  and  cause  of  the 
variation  in  the  share  of  the  product  of  industry  con- 
stituting general  wages.  In  the  present  chapter  we 
shall  he  concerned  with  the  second  of  these  funda- 
mental inquiries,  namely,  with  the  law  and  cause  of 
the  distribution  of  general  wages  among  the  members 
of  the  labor  group.  Our  point  of  departure  is  Pro- 
fessor Marshall's  treatment  of  the  topic. 

"We  may  then  regard  competition,  or,  to  speak 
more  exactly,  economic  freedom  and  enterprise,  as 
tending    to    make    time-earnings    in    occupations    of 

71 


72  Laws  of  Wages 

equal  difficulty  and  in  neighbouring  places  not  equal, 
but  proportionate  to  the  efficiency  of  the  workers."  l 
The  sense  in  which  Professor  Marshall  uses  the  word 
"  efficiency  "  is  to  be  inferred  from  the  context.  He 
defines  "  efficiency-wages "  as  "  earnings  measured, 
not  as  time-earnings  are  with  reference  to  the  time 
spent  in  earning  them ;  and  not  as  piece-work  earn- 
ings are  with  reference  to  the  amount  of  output  re- 
sulting from  the  work  by  which  they  are  earned  ; 
but  with  reference  to  the  exertion  of  ability  and  effi- 
ciency required  of  the  worker."  '2  In  the  fourth  book 
of  the  Principles  of  Economics,  Chapter  V  opens  with 
this  sentence :  "  We  have  next  to  consider  the  con- 
ditions on  which  depend  health  and  strength,  physical, 
mental  and  moral.  Thev  are  the  basis  of  industrial 
efficiency,  on  which  the  production  of  material  wealth 
depends."  Elsewhere,3  Professor  Marshall  asserts 
"  that  what  makes  one  occupation  higher  than  an- 
other, what  makes  the  workers  of  one  town  or  coun- 
try more  efficient  than  those  of  another,  is  chiefly  a 
superiority  in  general  sagacity  and  energy  which  is 
not  specialized  to  any  one  trade."  From  these  refer- 
ences it  may  be  inferred  that  the  term  "  efficiency ': 
when  applied  in  the  theory  of  wages  in  a  subjective 
sense 4  means  a  balance  of  physical,  mental,  and  moral 

1  Principles  of  Economics.     4th  edit.,  p.  6-50. 

2  Ibid.,  pp.  630-631.  3  Ibid.,  p.  286. 

4 The  word  "efficiency"  is  one  of  a  large  group  of  terms  —  such 
as  belief,  truth,  probability  —  in  which  there  is  ambiguity  due  to  their 
hiiving  both  a  subjective  and  an  objective  connotation.  The  two 
meanings  of  "efficiency"  in  the  theory  of  wages  should  be  carefully 
discriminated. 


Wages  and  Ability  73 

qualities,   which    is  felicitously   summarized  in   the 

phrase  "general  sagacity  and  energy." 

Is  there  any  ground  for  believing  that  this  general 
theory  has  any  relation  whatever  to  the  conditions 
of  wage  receiving  in  actual  industry?  Suppose  the 
relevancy  of  the  theory  were  denied,  —  as  indeed 
it  is  denied  frequently  and  vehemently,  —  how  could 
one  proceed  to  fortify  it  otherwise  than  by  reverting 
to  remote  hypothetical  premises  and  repeating  the 
long  chain  of  logical  deductions  ?  If  the  theory  is 
to  be  accepted  as  a  law,  using  the  word  law  in  the 
sense  of  our  first  chapter,  it  must  rest  upon  the 
concrete  facts  of  industry. 

A  similar  position  is  to  be  assumed  in  approaching 
the  explanation  of  wages  from  the  inductive  side. 
The  conclusion  upon  this  topic  of  the  Trench  Office 
du  Travail,  in  its  voluminous  report  on  wages  for 
1893-1897,  is  summarized  in  these  words :  "  On 
voit  entre  quelles  limites  etendues  varie  la  valeur 
relative  du  salaire  dans  les  diverses  professions. 
Cette  valeur  relative  depend  essentiellement  de  la 
rarete  des  aptitudes  intellectuelles  et  physiques 
necessaires  a  l'ouvrier,  du  degre  de  developpement 
de  ces  memes  aptitudes  qu'exigent  les  diverses  pro- 
fessions." l 

It  is  entirely  true  that  one  does  see  from  the  statis- 
tical schedules  that  there  is  a  wide  variation  in  rel- 
ative was;es,  but  in  the  whole  of  the  four  volumes 
of  the  report  there  is  not  a  word  to  show  a  quant  i- 

1  Salaires  et  duree  du  travail  <I<nts  Vindustrit  franfaise.     Vol.  I,  p.  512. 


7  I  Laws  of  Wages  , 

tative  relation  between  the  amount  of  washes  and 
"la  rarete  des  aptitudes  intellectuelles  et  physiques" 
of  the  laborer.  So  far  as  the  use  of  words  is  con- 
cerned, administrative  inquiry  and  pure  theory  take 
common  ground.  Would  it  be  possible  through  the 
discovery  of  an  economic  law  to  bring  the  two  to- 
gether so  that  the  theory  might  organize  the  data 
and  the  data  support  the  theory  ? 

An  Hypothesis  as  to  the  Distribution  of  Ability. 

Before  we  can  establish  a  quantitative  relation  be- 
tween wages  and  ability  we  must  have  an  hypothesis 
as  to  the  distribution  of  ability  among  a  representa- 
tive class  of  laborers.  The  particular  hypothesis 
that  is  put  forward  in  this  chapter  is  that  industrial 
ability  —  general  sagacity  and  energy  —  is  distrib- 
uted according  to  the  normal  or  Gaussian  law. 

The  normal,  or  Gaussian,  law  is  represented  graph- 
ically in  Figure  11  by  either  of  the  two  curves 
AMB,  arrib.  If  from  a  homogeneous  group  of 
men  a  large  number  of  measurements  of  any  physical 
character  are  made,  for  example  of  stature,  it  will 
be  found  that  the  measurements  may  be  arranged 
in  such  a  way  that  the  relative  frequencies  of  the 
deviations  from  the  average  measurement  will,  when 
plotted,  produce  a  curve  approximating  this  type. 
A  deviation  in  excess  of  the  average  stature  is 
measured  to  the  right  of  point  0,  on  the  line  ox, 
and  the  corresponding  frequency  of  the  deviation 
is    then   plotted    perpendicularly    at  the  end  of  the 


Wages  <i  in  I  Ability 


75 


76  Laws  of  Wages 

deviation.  Similarly,  deviations  below  the  average 
are  measured  to  the  left  of  point  0.  The  two 
sides  of  the  curve  are  symmetrically  disposed  about 
the  maximum  ordinate,  and  the  scatter  of  the  meas- 
urements about  this  ordinate  varies  with  the  stand- 
ard deviation  of  the  measurements.  The  standard 
deviation  of  the  curve  amb  is  twice  that  of  the 
curve  AMB. 

Grounds  for  the  Hypothesis. 

In  justification  of  the  hypothesis  that  has  just  been 
described  the  following  considerations  are  offered :  — 

(1)  The  accumulation  of  a  great  number  of  meas- 

urements of  physical  characters,  which  was 
begun  by  Quetelet  and  is  now  carried  for- 
ward with  zeal  by  anthropologists  and  bio- 
metricians,  has  established  that  physical 
qualities  are  distributed  according  to  the 
Gaussian  law.  "  We  have  very  definite  evi- 
dence that  the  normal  curve  suffices  to  de- 
scribe within  the  limits  of  random  sampling 
the  distribution  of  the  chief  physical  charac- 
ters in  man."  ' 

(2)  Several   years    ago  Sir    Francis  Galton  began 

his  studies  of  inheritance  on  the  assumption 
that  the  mental  and  moral  qualities  of  man 
are  distributed  according  to  the  same  law 
as  are  physical  qualities.  Professor  Pear- 
son's laborious  investigations  of  mental  char- 

1  Karl  Pearson  :  Biometrika,  Vol.  II,  p.  395. 


Wages  and  Ability  77 

acters  proceeds  upon  the  same  assumption: 
"  We  have  .  .  .  selected,  as  the  normal 
scale  of  intelligence,  that  which  would  be 
given  if  the  frequency  distribution  of  intelli- 
gence followed  the  normal,  or  Gaussian, 
curve  of  errors.  Whatever  the  true  scale 
may  be,  it  can  only  be  a  more  or  less  -  -  prob- 
ably less  —  distorted  form  of  this  scale."  * 
(3)  It  has  been  pointed  out  that  industrial  effi- 
ciency is  dependent  upon  physical,  mental, 
and  moral  qualities,  and  these  qualities,  ac- 
cording to  the  preceding  paragraphs,  there 
is  good  reason  for  regarding  as  being  dis- 
tributed according  to  the  Gaussian  law. 
Professor  Edgeworth  has  demonstrated  a 
theorem  to  the  effect  that  "  ...  if  a  varia- 
ble thing  obey  the  normal  law,  a  function 
of  that  tiling  will  obey  the  normal  law/'  - 
Professor  Edgeworth  however  gives  the  warn- 
ing that  "  this  property  holds  only  com- 
monly, not  universally." 

1  Karl  Pearson  :  Biometrika,  Vol.  V.  p.  106.  "  An  a  i>riori  justifica- 
tion of  the  scale  may  be  found  in  the  fact  that  the  plotted  points  of 
the  regression  curves  are  for  a  number  of  pairs  of  characters,  within 
the  limits  of  random  sampling,  on  a  straight  line  when  such  a  scale 
of  intelligence  is  used."     Ibid.,  pp.  106-107. 

2  Journal  of  the  Royal  Statistical  Society,  December,  1898,  p.  676. 


78  Laws  of  Wages 

The  Expression  of  the  Gaussian  Law  in  a  Form  that 
will  facilitate  the  Testing  of  the  Differential  Theory 
of  Wages. 

In  the  subsequent  part  of  this  chapter  we  shall 
refer  to  the  theory  concerning  the  law  and  cause  of 
the  distribution  of  general  wages  among  the  members 
of  the  labor  group  as  the  differential  theory  or  the 
differential  hypothesis  of  wages. 

The  statement  of  the  differential  hypothesis  by  the 
most  approved  authorities  contains  four  leading  prop- 
ositions :  — 

(1)  The  labor  force  in  a  country  of  varied  indus- 

tries is  a  force  of  varying  efficiency  per  la- 
borer unit ; 

(2)  The  character  of  the  industrial  organization  of 

a  particular  time  and  place  determines  the 
nature  and  degree  of  segregation  of  laborers 
into  groups  of  varying  efficiency.  The  two 
most  fundamental  groups  are  those  of  skilled 
and  of  unskilled  labor  ; 

(3)  The  laborer  of  least  efficiency  in  each  group 
receives  a  wage  which  constitutes  the  mini- 
mum wage  of  the  group.  This  minimum 
wage  is  not  less  than  the  highest  wage  that 
could  be  earned  by  the  least  efficient  mem- 
ber of  the  group  in  the  other  forms  of  em- 
ployment which  are  open  to  him ; 

(4)  The  more  efficient  laborers  within  a  group  re- 
ceive the  minimum  wage  of  the  group  plus 


Wages  and  Ability  «'.» 

a  supplement  proportionate  to  the  excess  of 
their  elliciency  over  that  of  the  least  capable 
laborer  in  the  same  group. 

We  have  assumed  that  the  distribution  of  ability 
among  a  large  group  of  laborers  follows  the  Gaussian 
law.  But  this  law  is  a  generalization  applying  to  an 
infinite  number  of  measurements,  whereas  the  statis- 
tics of  wages  are  available  for  only  a  finite  number  of 
laborers.  Furthermore,  according  to  the  differential 
hypothesis,  wages  are  distributed  among  laborers 
proportionately  to  their  differential  ability.  But  the 
Gaussian  law  gives  the  law  of  the  distribution  of 
ability  for  the  aggregate  of  laborers  :  it  does  not  de- 
scribe how  the  individuals  in  the  aggregate  differ  from 
each  other.  It  is  therefore  necessary  to  derive  from 
the  Gaussian  law  a  formula  that  will  be  applicable  to 
a  finite  group  and  will  express  the  average  differences 
in  ability  among  the  members  of  such  a  group. 

In  1902  Sir  Francis  Galton  proposed  to  British 
mathematicians  this  problem  :  "  A  certain  sum,  say 
<£100,  is  available  for  two  prizes  to  be  awarded  at  a 
forthcoming  competition  ;  the  larger  one  for  the  first 
of  the  competitors,  the  smaller  one  for  the  second. 
How  should  the  £100  be  most  suitably  divided  be- 
tween  the  two?  What  ratio  should  a  first  prize  bear 
to  that  of  a  second  one  ?  Does  it  depend  on  the 
number  of  competitors,  and  if  so,  in  what  way  ? 
Similiar  questions  may  be  asked  .  .  .  when  the 
number  of  prizes  exceeds  two.     What  should  be  the 


80  Laws  of  Wages 

division  of  the  £100  when  three  prizes  are  to  be 
given,  or  four,  or  any  larger  number  ?  "  1  Mr.  Gal- 
ton's  investigation  suggested  "  that  when  only  two 
prizes  are  given  in  any  competition,  the  first  prize 
ought  to  be  closely  three  times  the  value  of  the 
second."  The  novelty  and  interest  of  the  problem 
led  him  to  conclude :  "  I  now  commend  the  subject 
to  mathematicians  in  the  belief  that  those  who 
are  capable,  which  I  am  not,  of  treating  it  more 
thoroughly,  may  find  that  further  investigations  will 
repay  trouble  in  unexpected  directions." 

Professor  Karl  Pearson  answered  the  appeal  to 
mathematicians  and  undertook  the  solution  of  the 
problem  in  this  general  form  :  "  A  random  sample  of 
n  individuals  is  taken  from  a  population  of  JST 
members  which  when  JSf  is  very  large  may  be  taken 
to  obey  any  law  of  frequency  expressed  by  the  curve 
y  =  N<f>{x),  yclx  being  the  total  frequency  of  individ- 
uals with  characters  or  organs  lying  between  x  and 
x  +  dx.  It  is  required  to  find  an  expression  for  the 
average  difference  in  character  between  the  pth  and 
the  (p  + 1)"'  individuals  when  the  sample  is  arranged 
in  order  of  magnitude  of  the  character." 

"  I  propose  to  call  this  general  problem  :  Francis 
Gallons  Individual  Difference  Problem  in  Statistics, 
or,  more  briefly,  Galtons  Difference  Problem.  It  will 
be  seen  at  once  to  carry  us  from  the  consideration  of 
the  means  and  standard  deviations  of  mass  aggregates 

1  Francis  GaHxm,  F.K.S.:  "The  most  Suitable  Proportion  between 
the  Values  of  First  and  Second  Prizes."     Biometrika,  Vol.  T,  p.  385. 


Wages  and  Abilif;/  81 

and  arrays  to  the  average  interval  between  individuals 
of  those  aggregates.     We  may  still  deal  with  averages, 
but  we  fix  our  attention  no  longer  on  the  whole  pop- 
ulation, but  on  definite  individuals  in  its  ordered  array. 
This   I    believe   to  be    a    real   advance   in  statistical 
theory."    The  solution  of  the  problem  "  provides  us  for 
the  first  time,  I  believe,  with  most  probable  relation- 
ships between  individuals  forming  a  random  sample."  J 
One  would  think  that  this  mathematical  problem 
bad  been  formulated  and  solved  with   a  view  to  the 
application  of  the  results  to  our  problem  of  the  dif- 
ferential hypothesis  of  wages!     For  the  knowledge 
of  the  average  difference  in  ability  between  each  of 
1000  laborers  and  his  less  efficient  neighbor,  when  the 
whole  number  are  ranked  according  to  their  ability, 
would  afford  data  for  determining  the  average  dif- 
ference in  ability  of  the  999  laborers  over  their  least 
efficient  associate.     Moreover,  if   the   1000   laborers 
were  separated  into  two  groups,  the  one  composed  of 
the  less  efficient,  and  the  other  the  more  efficient,  thus 
giving  rise  to  a  minimum  wage  in  each  group,  the 
knowledge  of  the  average  difference  in  efficiency  in 
the  population  of  1000  would  suffice  for  the  computa- 
tion  of  the  average   difference   in   efficiency   of  the 
members  in  each  group  over  that  of  the  least  efficient 
member  of  the  same  group.     To  solve  our  problem  of 
wages,  the  first  need  is  the  construction  of  a  Standard 
Population  in  which  the  average  differences  in  ability 

1  Karl  Fearson  :  "  Note  on  Francis  Galton's  Problem."    Biometrika, 
Vol.  I,  pp.  390-399. 

G 


82  Laws  of  Wages 

of  its  members  are  computed.  Such  a  Standard 
Population,  judiciously  used,  would  supply  the  means 
with  which  to  obtain  a  first  approximation  to  the 
solution  of  several  questions  in  the  dynamics  of 
wages. 

The  Standard  Population. 

In  the  Appendix  to  this  chapter  are  two  mathe- 
matical tables:  Table  I,  Average  Differential  Ability 
in  a  Population  of  One  Hundred ;  Table  II,  Standard 
Population  of  One  Hundred.  A  detailed  account  of 
the  construction  of  these  tables  is  given  in  the  Ap- 
pendix. Before  proceeding  to  the  description  of 
Table  II,  upon  which  the  investigation  of  this  chapter 
is  based,  it  may  be  observed  that  Table  I  enables  us 
to  answer  the  question  as  to  the  form  of  distribution 
of  wages  when  the  incomes  of  laborers  are  apportioned 
entirely  according  to  ability.  For  example,  in  1900, 
in  the  manufactures  of  the  United  States,  the  average 
wage  of  males  over  sixteen  years  of  age  was  $11.43 
per  week.  The  aggregate  received  by  a  population 
of  100  would  therefore  be  $1143.  Assuming  the 
minimum  wage  to  be  $3.13  l  then,  if  wages  were  dis- 
tributed entirely  according  to  ability,  each  of  the 
more  sagacious  and  energetic  laborers  would  receive 
the  minimum  wage  $3.13,  plus  a  supplement  propor- 
tionate to  his  differential  ability.  That  is  to  say,  99 
laborers  would  each  receive  $3.13  plus  a  share  of 
$  830  (1143  -  313),  which  would  vary  proportionately 

1  The  reason  for  this  assumption  will  appear  later. 


Wages  and  Ability  s'-> 

to  the  excess  of  his  ability  over  that  of  the  lea.-t  capa- 
ble member  of  the  group.  The  $830  would  there- 
fore be  distributed  according  to  the  conditions  of 
columns  IV  and  VI II  in  Table  I.  The  ablest  man 
would  receive  $3.13  plus  (830)  (.02)  which  is  $3.13 
plus  J  16.60  =$19.73.  Similarly,  the  wages  of  the 
other  laborers  would  be  ascertained.  A  graphic  de- 
scription of  the  resulting  distribution  is  given  in  the 
accompanying  Figure  12,  where  wages  are  taken  upon 
the  axis  of  x  and  the  relative  frequencies  of  the  sev- 
eral rates  of  wages  are  plotted  parallel  to  the  axis  of 
y.  The  Gaussian  curve  traced  upon  the  figure  is 
practically  an  exact  fit 1  to  the  data. 

Table  II,  The  Standard  Population  of  One  Hundred, 
is  designed  to  meet  the  difficulty  of  the  segregation  of 
labor,  in  actual  industry,  into  groups  of  skilled  and 
of  unskilled  labor.     It  is  based  upon  the  knowledge  of 
the  average  differences  in  ability  between  members 
of  a  group  of  100.     The  total  population  of  100  is 
divided  into  an  upper  group  corresponding  to  skilled 
labor,  composed  of  the  fifty  ablest  members ;  and  a 
lower  group   corresponding  to  unskilled  labor,  com- 
posed of  the  less  capable  members.     The  two  groups 
are  then  treated  separately,  just  as  the  whole  popula- 
tion was  treated  in  Table  I;  that  is  to  say,  each  group 
of  fifty  is  considered  as  forming  a  separate  population. 
The  average  differences  in  ability  of  the  fifty  ablest 
members  over  the  ability  of  the  fifty-first  member  — 

1  According  to  the  Pearsoniau  test,  nx  =  17  and  yj  -  .942782,  which 
is  a  perfect  fit. 


8-i 


Laws  of  Wages 


£i/auoqe/jo  efie/uaus^/ 


Wages  and  Ability  85 

who  is  the  ablest  member  of  the  lower  group —  are  then 
computed.  Likewise  the  average  differences  in  ability 
of  the  members  of  the  lower  group  over  the  ability  of 
the  least  capable  member  of  that  group  are  ascertained. 
In  columns  III  and  VII  these  differences  are  expressed 
in  terms  of  the  standard  deviation  of  the  group,  and 
in  columns  IV  and  VIII  the  same  individual  differ- 
ences are  respectively  expressed  as  percentages  of  the 
sum  of  the  differences.  The  method  in  which  this 
table  is  used  to  bring  to  a  statistical  test  the  differ- 
ential hypothesis  as  to  the  distribution  of  wages  will 
now  be  rendered  clear  by  means  of  examples. 

The  Application  of  the  Tlteory  of  the  Standard  Popu- 
lation. 

Certain  principles  must   be   observed  in  selecting 
data  to  test  the  theory  :  — 

(1)  The  differential  hypothesis  is  based  upon  the 
assumption  of  perfect  competition  of  laborers. 
To  meet  this  specification,  (a)  we  have  taken 
data  only  from  adult  male  laborers  in  man- 
ufacturing industries,  where  competition 
among  laborers  is  keenest,  and  (b)  have 
made  a  supplementary  hypothesis  —  designed 
to  meet  the  difficulty  of  non-competing 
groups  —  to  the  effect  that  the  labor  force  is 
divided  into  two  groups,  the  members  of 
each  of  which  receive  the  minimum  wage  of 
their  respective  groups  plus  a  supplement 
proportionate  to  their  differential  ability. 


86  Laws  of  Wages 

(2)  The   differential   hypothesis    is   based    on    the 

assumption  of  conditions  of  wage  earning 
in  a  limited  area  —  '"in  neighboring  places," 
to  use  Professor  Marshall's  phrase.  Ac- 
cordingly, in  order  to  avoid  complications 
of  differences  due  to  geographical  separa- 
tion, the  following  data  refer,  as  far  as  pos- 
sible, to  conditions  in  homogeneous  areas. 

(3)  The  differential  hypothesis  is  based  upon  the 

assumption  that  opportunities  for  work  are 
sufficiently  varied  to  permit  each  laborer  to 
exploit  to  the  full  his  special  degree  of  sa- 
gacity and  energy.  By  confining  the  selec- 
tion of  data  to  general  manufactures  instead 
of  particular  trades,  this  condition  of  the 
theory  is  approximated. 

We  shall  now  consider  in  detail  the  application  of 
the  theory. 

(a)  Wages  in  France. 

In  Vol.  I  of  the  report  of  1893  on  Salaires  et 
(hirer  du  travail  tin  us  I  'Industrie  francaise,  p.  496, 
there  is  the  following  table  giving  the  distribution 
of  wages  in  the  Departement  de  la  Seine :  — 


W ti yes  and  Ability 


87 


TABLE  I.  —  Distribution  of  Laborers   according  to   Bates 
hi    Wages  per  Day.     France 


Rats  in  Fb  inob 

N  imi:i  \: 

K  m  I.   in    Fbani  8 

Nimiiki: 

2.75  and  less 

173 

7.25-  7.75 

1,359 

2.75-3.25 

137 

7.75-  8.25 

552 

3.25 -3.75 

153 

8.25-  8.75 

232 

3.75-1.25 

1.172 

8.75    9.25 

133 

1.25    1.75 

1,271 

9.25-  9.75 

73 

L  7  5-5. 2  5 

2,1 82 

9.75-10.25 

137 

5.25  -5.75 

1.351 

10.25-11.25 

30 

5.75-6.25 

1,551 

11.25-1-J.25 

15 

6.25-6.75 
6.75-7.25 

1,403 
1.558 

.More  than  12.25 
Total 

19 

13,804 

This  table  describes  the  actual  conditions  of  wage 
receiving  among  13,804  representative  workmen. 

In  order  to  apply  the  differential  hypothesis  we 
must  first  settle  upon  the  wage  to  be  used  as  a  mini- 
mum wage  in  the  lower  group  of  the  Standard  Popu- 
lation. The  total  range  of  the  Standard  Population 
of  One  Hundred  is  5.02  times  the  standard  deviation 
(2.52  +  2.50),  which  gives  a  half-range  of  2.51  times 
the  standard  deviation.  If,  now.  we  refer  to  a  table 
of  the  values  of  the  probability  integral  in  terms  of 
the  standard  deviation, '  we  find  that,  on  the  average, 
six  cases  in  a  thousand  exceed  2.51  times  the  stand- 
ard deviation.  Consequently,  in  order  to  make  the 
Standard  Population  of  One  Hundred  applicable  to 
the  French  schedule  affecting  13,804  laborers,  we 
have  substracted  from  each  end  of  the  total  series 
83  members,  that   is,   (.006)   (13,804).     This  would 

1  The  best  table  is  that  of  W.  F.  Sheppard  :  ••  New  Tables  of  the 
Probability  Integral."     Biometrika,  Vol.  II,  pp.  174-190. 


88 


Laws  of  Wages 


leave  90  members  in  the  lowest  group  and  118  in  the 
group  9.75  —  10.25.  If  the  lowest  limit  of  actual 
wages  be  supposed  to  be  2  francs,  we  should  then 
find  the  theoretical  minimum  for  the  Standard  Popu- 
lation from  the  following  proportion  173:.75::83:x. 
As  x  in  this  proportion  is  36  centimes,  the  theoreti- 
cal minimum  wage  is  2.36  francs.  Similarly,  the 
superior  limit  of  wages  in  the  actual  figures  would 
be  reduced  to  10.18  francs.  The  modified  schedule 
would  then  appear  as  in  the  first  and  second  columns 
of  the  following  table  :  — 

TABLE  II.  —  Percentage  Distribution  of  Laborers  according 
to  Daily  Rates  of  Wages  in  the  Departement  de  la  Seine 
and  in  the  Standard  Population 


Department  de  la  S 

EINE 

Standard  1 

OPULATION 

1 

ii 

III 

IV 

V 

Rate  in  Francs 

Number 

Percentage 

Kate  in  Francs 

Number 

2.55 

90 

.66 

2.36 

1 

3.00 

137 

1.00 

3.00 

o 

3.50 

453 

3.33 

3.50 

4 

4.00 

1172 

8.59 

4.00 

6 

4.50 

1271 

9.32 

4.50 

10 

5.00 

2182 

16.00 

5.00 

13 

5.50 

1351 

9.91 

5.50 

14 

6.00 

1551 

11.38 

6.00 

12 

6.50 

1403 

10.29 

6.50 

11 

7.00 

1558 

11.42 

7.00 

9 

7.50 

1359 

9.96 

7.50 

7 

8.00 

552 

4.05 

8.00 

4.5 

8.50 

2:12 

1.70 

8.50 

'    3.5 

9.00 

133 

.97 

8.98 

1 

9.50 

76 

.56 

9.31 

1 

9.96 

118 

.86 

9.91 

1 

Total 

13638 

100.00 

Total 

100 

Wages  and  Ability  89 

Having  determined  the  theoretical  minimum  wage 

for  the  Standard  Population,  we  now  find  by  means 
of  the  first  and  third  columns  in  the  above  Table  II 
that  the  average  wage  in  the  manufactures  of  the 
Dipartement  de  la  Seine  was  5.864  francs  per  day, 
and  that  the  first  fifty  per  cent  of  the  laborers  — 
that  is  the  less  capable  laborers — received  39.819  per 
cent  of  the  total  wage  dividend.  These  three  facts, 
to  wit :  (1)  the  theoretical  minimum  wage  of  the 
Standard  Population  (2)  the  average  wage,  and  (3) 
the  percentage  of  the  wage  dividend  received  by  the 
less  capable  group,  are  all  the  facts  that  are  neces- 
sary in  order  to  apply  at  once  the  theory  of  differen- 
tial wages. 

We  shall  now  proceed  to  determine  what  the  dis- 
tribution would  be  according  to  the  theory  of  reward 
in  proportion  to  ability  and  shall  then  compare  the 
theoretical  distribution  with  the  actual  distribution. 

Since  the  average  wage  is  5.864  francs,  the  whole 
wage  dividend  to  be  shared  by  the  Standard  Popula- 
tion of  One  Hundred  is  586.40  francs.  As  the  less 
capable  group  receives  39.819  per  cent  of  the  total 
dividend,  the  first  fifty  members  of  the  Standard  Pop- 
ulation will  divide  between  them  233.50  francs,  and 
the  more  capable  fifty  will  receive  586.40  —  233.50  = 
352.90  francs.  The  minimum  wage  in  the  less  eiti- 
cient  group  is  2.36  francs,  and  since,  according  to  the 
diiferential  hypothesis  each  of  the  fifty  members  of 
this  group  will  receive  the  minimum  wage  of  the 
group  plus  a  supplement   proportionate    to   his    dif- 


90  Laws  of  Wages 

ferential  ability,  the  total  amount  to  be  divided 
among  the  fifty  laborers  in  the  form  of  supplemen- 
tary payment  is  233.50-  (50)  (2.36)  =  115.50  francs. 
The  resulting  distribution  in  this  group  will  therefore 
be  computed  by  means  of  column  VIII  in  Table  II 
of  the  Appendix  to  this  chapter.  For  example,  the 
fifty-first  laborer  —  who  is  the  ablest  member  of  the 
less  capable  group  —  will  receive  2.36  +  (115.50) 
(.029083)  =  2.36 +  3.3591  =  5.72  francs.  In  a  simi- 
lar manner  the  amounts  received  by  the  other  mem- 
bers of  this  group  may  be  computed. 

The  dividend  of  the  more  capable  group  is  352.90 
francs.  (  The  minimum  wage  of  the  group  is  the 
highest  wage  that  could  be  earned  in  the  lower 
group,  which,  as  we  have  just  seen,  is  5.72  francs. 
This  method  of  estimating  the  minimum  wage  of  the 
more  efficient  group  is  regarded  as  in  harmony  with 
actual  practice  where  the  minimum  wage  in  a  group 
is  equal  to  the  highest  wage  that  could  be  earned  in 
other  forms  of  employment  open  to  the  laborer.   / 

According  to  the  differential  hypothesis  the  mem- 
bers of  the  abler  group  receive  likewise  the  minimum 
wage  of  their  group  plus  a  supplement  proportionate 
to  their  differential  ability.  As  the  minimum  wage 
is  5.72  francs,  and  the  total  amount  shared  is  352.90 
francs,  the  amount  distributed  in  the  form  of  sup- 
plementary payments  is  352.90  — (50) (5. 72)  =  66.90 
francs.  This  sum  66.90  francs  is  distributed  accord- 
ing to  Table  II  of  the  Appendix,  column  IV.  For 
example,  the  ablest  member  of  the  Standard  Popula- 


Wages  and  Ability  91 

tion  receives  as  total  wage  5.72 +  (66.90)  (.062670)  = 
5.72  +  4.1926  =  9.91.  The  fiftieth  laborer  receives 
5.72 +  (66.90)  (.000622)  =  5.72 +  .0416  =  5.76  francs. 
The  wages  of  the  other  members  of  the  more  efficient 
group  are  computed  in  the  same  way.  The  resulting 
distribution  of  wages  in  the  total  Standard  Popula- 
tion may  be  seen  in  columns  IV  and  V  of  Table  II 
printed  in  the  text. 

To  what  degree  is  the  differential  hypothesis  of 
wages  borne  out  by  the  facts  of  wage  receiving  in  the 
French  Dd parte  meat  ?  If  the  figures  in  Table  II  for 
the  actual  distribution  of  wages  in  the  Departement 
de  la  Seine  and  for  the  distribution  in  the  Standard 
Population  were  plotted  just  as  they  are,  it  would 
be  seen  that  the  approximation  is  very  close,  but, 
because  of  the  zigzag  shape  assumed  by  each  series  of 
figures,  the  measure  of  the  degree  of  approximation 
would  be  rather  vague.  The  result  of  the  method 
which  I  have  adopted  to  bring  out  the  degree  of  ac- 
cordance between  fact  and  theoiy  may  be  seen  by 
referring-  to  Figure  13.  In  this  figure  the  zigzag 
line  gives  the  actual  percentage  frequencies  of  wages 
as  they  appear  between  limits  2.36  and  10.18  in  the 
French  report.  The  dashed  smooth  curve,  computed 
by  Professor  Pearson's  method  of  moments,  is  the 
curve  fitting  best  the  actual  figures.  The  continuous 
smooth  curve  is  the  best  fit  to  the  tabulated  wages  of 
the  Standard  Population.  The  fact  that  the  smooth 
curve  of  the  actual  data  is  practically  congruent  with 
the  smooth  curve  of  the  Standard  Population  shows 


92 


Laws  of  Wages 


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Wages  and  Ability  93 

• 

that  in  this  particular  case,  a  doctrine  of  pure  econom- 
ics is  statistically  verified.  "  La  valeur  relative  du 
salaire  .  .  .  depend  essentielleinent  de  la  rarete  des 
aptitudes  intellectuelles  et  physiques  necessaires  a 
Touvrier,  du  degre  de  developpement  de  ces  in  ernes 
aptitudes  qu'exigent  les  diverses  professions."  The 
words  of  the  French  report  are  now  the  accurate  de- 
scription of  an  economic  law. 

(b)    Wages  in  Massachusetts. 

As  the  distribution  of  wages  in  the  Departement  de 
la  Seine  presents  only  a  small  degree  of  skewness,  we 
shall  offer  a  further  test  of  the  differential  theory  of 
wages  by  taking  a  case  in  which  the  distribution  is 
characterized  by  a  considerable  degree  of  asymmetry. 
Table  III  of  the  text,  which  exhibits  data  for  Massa- 
chusetts, has  been  constructed  in  a  similar  manner  to 
that  of  Table  II  referring;  to  the  Devartement  de  la 
Seine.  The  crude  data  of  the  table  were  taken  from 
the  Census  of  Manufactures,  1905,  Bulletin  93,  p.  109. 
Figure  14  illustrates  the  degree  of  correspondence 
between  theory  and  practice. 

Remark  upon  the  Preceding  Demonstration. 

The  equal  division  of  the  Standard  Population  of 
One  Hundred  into  two  groups  needs  justification. 
The  asymmetry  of  a  wage  curve  is  due  to  the  influence 
of  several  factors,  among;  which  are  the  relative  nura- 
bers  of  laborers  at  different  ages,  the  increasing  value 
of  high  degrees  of  efficiency  due  to  the  increasing  con- 


94 


Laws  of  Wages 


si/a^o^yo  atfe/ojju*?,-/ 


Wages  and  Ability 


95 


TABLE  III.  —  Percentage  Distribution  op  Laborers  accord- 
ing to  Weekly  Rates  of  Wages  in  Massachusetts  and  in 
the  Standard  Population 


\i  \--  \.  111  -i  pre 

Si  \ '.  D  \ui>    Po 

■I "i.A'l  ION 

I 

n 

in 

IV 

V 

Rate  in  Dollars 

Number 

Percentage 

[{ate  in  Dollars 

Number 

2.79 

1414 

.11 

2.58 

1 

3.50 

4176 

1.29 

3.68 

1 

4.50 

8920 

2.75 

4.50 

o 

5.50 

1:5,937 

4.31 

5.50 

4 

6.50 

22,104 

6.83 

6.50 

6 

7.50 

28,055 

8.06 

7.50 

9 

8.50 

28,425 

8.78 

s.5() 

11 

9.50 

39,951 

12.34 

9.50 

13 

10.50 

27,084 

8.36 

10.50 

8 

11.50 

24,705 

7.0:; 

11.50 

7 

12.50 

22,239 

6.87 

12.50 

0 

13.50 

1!  1.75  1 

O.lo 

L3.50 

6 

11.50 

17,216 

5.32 

14.50 

5 

15.50 

14,748 

4.55 

15.50 

5 

16.50 

12,603 

3.89 

10.50 

4 

17.50 

9958 

3.08 

17.5H 

3 

18.50 

S09S 

•J.  50 

18.50 

•> 

19.50 

6203 

L.92 

19.50 

•j 

20.50 

4541 

L.40 

20.50 

2 

21.50 

3164 

.98 

21.64 

1 

22.50 

2020 

.62 

22.81 

1 

23.50 

1162 

.30 

24.92 

1 

21.50 

loll 

.32 

25.50 

921 

.28 

20.50 

800 

.25 

27.40 

546 

.17 

Total 

323,785 

100.00 

Total 

100 

9G  Laws  of  Wages 

centration  of  industry,1  the  temporary  monopoly  of 
particular  grades  of  skill,  and  the  strategic  advantage 
in  bargaining  enjoyed  by  trade-unions.  It  is  not  pos- 
sible at  present  to  determine  how  far  these  factors 
are  respectively  effective  in  raising  wages,  and  the 
equal  division  of  the  Standard  Population  into  two 
groups  is  simply  a  means  of  giving  expression  to  the 
joint  effect  of  a  number  of  factors  whose  individual 
influence  has  not  vet  been  determined.  It  would  be 
more  philosophic  but  less  simple  to  assume  that  this 
"  joint  effect ':  to  the  advantage  of  efficient  laborers 
is  a  linear  function  of  their  differential  efficiency. 

1  See  Chapter  VI. 


Wages  and  Ability  97 


APPENDIX 

Notes  on  the  Construction  of  Table  I. 

I.  The  table  is  composed  of  eight  columns.     Columns 
I  and  V,  marked  p,  give  the  rank  of  the  individual  in  the 

total  population  of  100.     Columns  II  and  VI,  marked  — , 

give  the  difference  between  each  individual  and  the  next 
in  order  of  rank  divided  by  the  standard  deviation  of  the 
whole  group.  Columns  III  and  VII  give  the  difference, 
in  terms  of  the  standard  deviation,  between  each  individual 
of  the  group  and  the  last  member  of  the  group.  The  first 
entry  in  column  III  is  obtained  by  summing  the  entries  in 
columns  II  and  VI.  The  second  entry  in  III  is  obtained 
by  subtracting  from  the  first  entry  in  that  column  the  first 
entry  in  column  II.  Similarly  of  the  remaining  entries  in 
columns  III  and  VII.  Columns  IV  and  VIII  are  obtained 
by  expressing  each  entry  in  columns  III  and  VII  as  a  per- 
centage of  the  sum  of  the  entries  in  columns  III  and  VII. 
For  example,  the  total  of  columns  III  and  VII  is  251.4425, 
and  the  first  item  in  column  III,  5.02885,  is  .02  of  251.4425. 

II.  The  mathematical  derivation  of  —  is  explained  in 
the  "Notes  on  the  Construction  of  Table  II." 


98 


Laws  of  Wages 


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Wages  and  Ability  99 


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100  Laws  of  Wages 

Notes  on  the  Construction  of  Table  II. 

I.  The  table  is  composed  of  eight  columns.  Columns 
I  and  V,  marked  p,  give  the  rank  of  the  individual  in  the 

total  population  of  100.     Columns  II  and  VI,  marked  *?, 

s 

give  the  difference  between  each  individual  and  the  next 
in  order  of  rank,  divided  by  the  standard  deviation  of  the 
whole  group.  Column  III  gives  the  difference,  in  terms 
of  the  standard  deviation,  between  each  of  the  first  fifty 
members  of  the  group  and  the  fifty-first  member.  The 
first  entry  in  the  column  is  obtained  by  summing  the  en- 
tries in  column  II.  The  second  entry  in  column  III  is  ob- 
tained by  subtracting  from  the  first  entry  in  that  column 
the  first  entry  in  column  II.  Similarly  of  the  remaining 
entries  in  column  III.  Column  VII  is  constructed  from 
column  VI  in  the  same  way  that  column  III  is  constructed 
from  column  II.  Column  IV  is  obtained  by  expressing 
each  entry  in  column  III  as  a  percentage  of  the  sum  of 
the  entries  in  column  III.  Similarly  column  VIII  is  con- 
structed from  column  VII.  For  example,  the  total  of 
column  III  is  40.321478,  and  the  first  item  in  column  III, 
2.526958,  is  .06267  of  40.321478. 

II.  In  computing  the  successive  differences  between 
the  first  six  members  of  the  Standard  Population,  Pro- 
fessor Pearson's  formula  for  %p  was  used. 


V2  irp  ppe  p    1     ,  -,    .         .         .  > 

where  s  is  the  standard  deviation.      (See  Biometrika,  Vol. 
I,  p.  396,  formula  XXVII.) 

III.    Since,    by    Stirling's    formula,    when  p   is    large, 

I  p  =  V2tt»  ppe'p,  the  factor    v~irpppe  p ^  in  the  a^ove  for_ 

\JP_ 


Wages  and  Ability  If). 

mula  for  y^,,  approximates  to  unity  with  increasing  values 
of  p.  The  last  factor,  )  1  -|-  cx  +  e2  4-  ?3  •••  \,  seems  also  to 
approach  unity  as  p  increases.      When  p  =  5, 


V2 


7rPPPe~P  \1  +  Cl  +  c2  +  <y  (  =  .9897l>  1. 


It  has  consequently  been  thought  sufficient  for  the  ] im- 
poses   of    this    chapter    to   compute    %p   by    the    formula 

a 

v  = for   the   values  of  p  greater   than    5    and   less 

nym 

than  51. 

IV.    The  values  of  m,  which  were  needed  to  obtain  ym, 

were  computed  from  the  formula        — *-  =  * /—  I  e~ix'dx. 

n  \  7T  •/« 

(Ibid.,  p.  395,  formula  XII.)  In  making  these  compu- 
tations the  values  of  the  probability  integral  as  given  in 
Merrimans  Least  Squares  were  used.  The  table  was 
computed  several  years  ago  when  I  was  not  acquainted 
with  the  apparatus  for  making  easy  and  accurate  calcula- 
tions. The  values  of  m  and  ym  could  be  obtained  simul- 
taneously from  Sheppard's  Tables  (Biometrika,  Vol.  II, 
pp.  174-190),  by  using  the  formula3 


n 


—t-  =   I  =  e~*x~dx,  and  ym  =  —     -  e~*m . 

n         J-*>  V2tt  V2tt 

(Biometrika,  Vol.  I,  p.  395.) 

V.  The  degree  of  accuracy  of  the  tabic  is  not  so  givat 
as  it  appears  to  be  because,  in  the  evaluation  of  m.  Bar- 
low's tables  were  employed  in  the  calculation  of  squares, 
and  consequently  only  four  figures  were  used.  This  de- 
fect does  not  in  any  degree  invalidate  the  theoretical 
result  that  has  been  reached,  but  it  is  noted  here  as  a 
warning  to  others  who,  otherwise,  might  use  the  table  for 
a  purpose  requiring  greater  precision.     That  it   is  practi- 


102  Laws  of  Wages 

cally  accurate  for  present  purposes  follows  from  the  fact 
noted  in  the  chapter  that  when  the  distribution  of  wages 
is  calculated  by  Table  I  the  resulting  smooth  graph  is  a 
Gaussian  curve.  The  degree  of  fit,  when  subjected  to  the 
Pearsonian  test,  gives  n'  =  17  and  %2=  .942782,  which  is 
practically  a  perfect  fit. 


Wages  and  Ability 


Hi:; 


rI 

'ABLE    II  —  Standard  Population  of  One  Him 

(RED 

I 

n 

III 

IV 

V 

\  i 

\  11 

\  III 

Difference 

Difference 

Pero  i 

I  nil.  i.  nee 

Difference 

ntage 

p 

from  the 

of 

P 

*P 

from  the 

of 

K 

51st  Person 

40.3-.'  1478 

8 

100th  P 

1  122 

1 

.360964 

2.526958 

.002070 

51 

.025074 

2. 501  Si  12 

.029083 

2 

.200664 

2.165994 

.053718 

52 

.025098 

2. 470S is 

.028791 

3 

.144746 

1.965330 

.048741 

53 

.025137 

2.451720 

.028500 

4 

.114680 

1.820584 

.045152 

54 

.025192 

2.4205s:; 

.028207 

5 

.095994 

1.705904 

.042308 

55 

.02520,0 

2.401391 

.027915 

6 

.083843 

1.609910 

.039927 

56 

.025354 

2.376125 

.027621 

7 

.074499 

1.52MI07 

.037847 

57 

.025458 

2.350771 

.027326 

8 

.067258 

1.451568 

.036000 

58 

.025583 

2.325313 

.027030 

'.i 

.061599 

1.384310 

.034332 

59 

.025732 

2.299730 

.0207:;:; 

10 

.056909 

1.:  '.227 11 

.032804 

60 

.025881 

2.273998 

.026434 

11 

.053146 

1.265802 

.031393 

01 

.020001 

2.248117 

.026133 

12 

.049990 

1.212656 

.031X175 

62 

.026260 

2.222056 

.025830 

13 

.047250 

1.162666 

.028835 

63 

.026486 

2.195796 

.025525 

14 

.044  913 

1.115416 

.027663 

01 

.020725 

2.169310 

.025217 

15 

.042871 

1.070503 

.026549 

05 

.026994 

2.1425S5 

.024906 

lfi 

.041081 

1.027632 

.0251m; 

66 

.027287 

2.115591 

.024502 

17 

.039512 

.986551 

.024467 

07 

.027014 

2.088304 

.021275 

18 

.038131 

.947039 

.023487 

OS 

.027907 

2.01  0090 

.023954 

19 

.036854 

.908908 

.022542 

69 

.028347 

2.032723 

.023629 

'_'() 

.035700 

.872054 

.021628 

70 

.028755 

2.004376 

.02.;:  500 

21 

.034686 

.836354 

.020742 

71 

.029207 

1.975021 

.022!  105 

22 

.033769 

.801668 

.019882 

72 

.029710 

1.946414 

.022020 

23 

.032937 

.767899 

.019044 

73 

.030247 

1.9107 04 

.1  (22281 1 

24 

.032160 

.734962 

.018228 

74 

.030822 

1.886457 

.021929 

25 

.031479 

.702802 

.0174:50 

75 

.031479 

1.855635 

.021571 

26 

.().•',(  IS22 

.671323 

.010049 

7(5 

.0:52100 

1.824156 

.021205 

27 

.0:50217 

.040501 

.015885 

77 

.0:129:57 

1.791990 

.020831 

28 

.0211710 

.0111251 

.0151: 15 

78 

.033769 

1.759059 

.020448 

29 

.029207 

.580544 

.014398 

70 

.034686 

1.725290 

.020055 

30 

.028755 

.551337 

.01. -5074 

80 

.035700 

1.0901  04 

.019052 

31 

.028347 

.522582 

.012960 

81 

.036854 

1.654904 

i   .019237 

32 

.027967 

.494235 

.012257 

82 

.038131 

1.618050 

.018809 

33 

.027014 

.466268 

.011501 

83 

.039512 

1.579919 

!    .018366 

34 

.027287 

.438654 

.010879 

84 

.041081 

1.540407 

.017900, 

35 

.026994 

.411.107 

.010202 

85 

.042871 

1.499326 

.01 7429 

36 

.020725 

.384373 

.0005:;:; 

86 

.04491:5 

1.456455 

.016928 

37 

.026486 

.357648 

.008870 

87 

.047250 

1.411542 

.016408 

38 

.H2020O 

.331162 

.00821:5 

88 

.0499'.  tit 

1.364292 

.015859 

39 

.020(101 

.304902 

.007502 

89 

.053146 

1.314302 

.015278 

40 

.025881 

.2788 1 1 

.006915 

90 

.056909 

1.20,1150, 

.014660 

41 

.025732 

.000271 

91 

.061599 

1.204247 

.013999 

42 

.025583 

.227228 

.005635 

92 

.067258 

1.142648 

.013283 

4:; 

.025458 

.2010,45 

.005001 

93 

.074499 

1.075390 

.012501 

44 

.025354 

.176187 

.004370 

94 

.083843 

L.000891 

.01 1635 

45 

.025266 

.150833 

.003741 

95 

.0950!  it 

.917048 

,0106  0 

4<; 

.025192 

.125507 

.003114 

90 

.1140SO 

.821054 

.009544 

47 

.025137 

.100375 

.002489 

97 

.144740 

.706374 

.008211 

48 

.025098 

.075238 

.001866 

98 

.200644 

.561628 

.000529 

49 

.02f)074 

.050140 

.001244 

99 

.360964 

.360964 

.004190 

50 
Total 

.025000 

.0251  Xifi 

.000022 

2  520058 

10..12147S 



Total 

2.501S92 

86.026422 



CHAPTER   V 

WAGES   AND   STRIKES 

"  Ce  ne  sont  pas  les  greves  qui  rendent  corapte  des  variations  du 

salaire,  soit  par  leur  succes,  soit  par  leur  6chec,  maisce  sont  les  causes 

replies  de  variation  du  salaire  qui  se  manifestent  par  une  part  dans 

les  greves  et  rendent  compte  de  l'existence,  de  la  place  et  des  r6sultats 

de  ces  greves  meraes." 

—  Francois  Simiaxd. 

In  the  investigation  of  the  critical  question  of 
modern  industry  concerning  the  relation  of  wages  to 
strikes,  neither  of  the  extreme  theories  as  to  the 
nature  of  that  relation  will  be  adopted  as  an  exclu- 
sive working  hypothesis.  The  wage-fund  theorists 
will  not  be  followed  in  their  assumption  that  the  rate 
of  wages  is  determined .  by  inexorable  economic  laws, 
and  that  organizations  of  laborers  for  the  purpose  of 
increasing  wages  must  at  best  be  ineffectual,  while  as 
a  rule  they  would  prove  harmful.  Nor  will  the  mili- 
tant syndicalist  be  followed  in  the  assumption  of  an 
unlimited  power  of  labor  organizations  to  better  the 
economic  status  of  the  laborer.  The  one  hypothesis 
that  is  entertained  is  that  both  economic  law  and  trade 
combinations  affect  the  outcome  of  trade  disputes  as 
to  wages,  and  the  scientific  task  that  is  imposed  is  to 
measure,  as  far  as  possible  with  available  data,  the 
relative  importance  of  the  two  factors  in  the  deter- 
mination of  the  resulting  rate  of  wages. 

104 


Wages  and  Strikes  L05 

Preceding  chapters  have  shown,  not  theoretically 
but  concretely,  that  wages  move  pari  passu  with  the 
productivity  of  labor,  and  that  the  productivity  of 
labor  is  conditioned  by  the  degree  and  nature  of  the 
organization  of  capita]  and  labor  in  industry.  Does 
the  productivity  of  labor  likewise  set  bounds  to  the 
power  of  labor  organizations  to  raise  wages  ?  Does 
the  productivity  theory  of  wages  give  a  clew  to  regu- 
larities in  the  outcome  of  strikes  ?  Are  there  economic 
laws  of  strikes  ? 

In  this  chapter  an  attempt  will  be  made  to  obtain 
some  definite  idea  as  to  the  power  of  trades-unions  to 
raise  wages  and  as  to  the  limits  set  by  economic  law 
to  the  effective  activity  of  trades-unions.  The  in- 
quiry will  consequently  seek  answers  to  two  questions : 

(1)  as  to  the  manner  and  measure  in  which  trades- 
unions  influence  the  outcome  of  trade  disputes ;  and 

(2)  as  to  the  manner  and  measure  in  which  the  out- 
come of  trade  disputes  is  limited  by  economic  law. 

Outcome  of  Strikes  as  affected  by  Trades- Unions. 

If  it  be  true  that  labor  organizations  exert  an  in- 
fluence on  the  outcome  of  .strikes,  then  the  following 
conclusions  would  seem  to  be  necessary  corollaries : 
(1)  The  outcome  of  strikes  that  are  declared  by  labor 
organizations  should  be  more  favorable  to  the  interests 
of  laborers  than  the  outcome  of  strikes  that  are  not 
so  declared  ;  (2)  The  stronger  the  labor  organization 
in  an  industry,  the  more  favorable  to  the  interests  of 


106 


Laws  of  Wages 


the  laborer  should  be  the  outcome  of  strikes  that  are 
declared  by  labor  organizations  in  the  industry. 
These  two  conclusions  we  shall  test  with  the  avail- 
able data. 

The  material  used  in  the  treatment  of  most  of  the 
topics  discussed  in  this  chapter  may  be  found  in  the 
volume  on  Strikes  and  Lockouts  that  was  issued,  in 
1906,  as  the  Twenty-First  Annual  Report  of  the  Com- 
missioners of  Labor,  for  the  United  States.  This 
volume  will  be  referred  to,  simply,  as  the  Report. 

TABLE  I. —  Correlation  between  the  Outcome  of  Strikes 
and  the  Ordering  or  not  Ordering  of  Strikes  by  Labor 
Organizations 


Outcome  of  Strikes 
Establishments  in  which  Strikes 

Total 

Succeeded 

Succeeded 
Partly 

Failed 

Ordered  by 

Labor 

Organizations 

80,772 

25,916 

56,563 

163,251 

Not  ordered 
by  Labor 

Organizations 

5927 

1720 

9857 

17,504 

Total 

86,699 

27,636 

66,420 

180,755 

Table  I  of  the  present  chapter,  which  was  compiled 
from  pages  490-491  of  the  Report,  presents  material 
pertinent  to  an  investigation  as  to  whether  the  results 
of  strikes  ordered  by  labor  organizations  are  more 
favorable  to  the  interests  of  laborers  than  the  results 


Wages  and  Strikes  107 

of  strikes  that  are  not  so  ordered.  The  table  gives  a 
summary  of  the  results  of  strikes  in  the  United  States 
from  1881  to  1905. 

The  method  that  is  employed  to  measure  the  rela- 
tion between  the  two  variables  —  the  outcome  of 
strikes  and  the  ordering  or  not  ordering  of  strikes 
by  labor  unions --is  the  method  that  has  recently 
been  invented  by  Professor  Pearson 1  for  the  evalua- 
tion of  the  "  correlation  ratio,"  which  is  symbolized 
by  the  Greek  letter  rj.  The  method  is  applicable 
to  problems  like  the  one  presented  in  Table  I,  on 
condition  that  one  of  the  variables  may  be  assumed 
to  be  distributed  according  to  the  Gaussian  law. 
The  method  affords  a  good  first  approximate  measure 
of  relation  when  the  distribution  of  the  variable  is 
slightly  skew.  The  arithmetical  value  of  7),  like  the 
coefficient  of  correlation,  varies  from  zero  to  unity. 

In  making  the  computation  in  the  particular  case 
of  Table  I,  it  has  been  assumed  that  the  alternative 
variable  —  "ordered  by  labor  organizations"  and 
"not  ordered  by  labor  organizations"  —  is  distrib- 
uted according  to  the  normal  law.  Some  justifica- 
tion of  the  assumption  is  found  in  the  definition  of 
the  terms  by  the  Bureau  of  Labor.  "  The  number 
of  strikes  ordered  by  labor  organizations  includes 
all  strikes  ordered  by  direct  vote  of  a  labor  organi- 
zation and  also  all  ordered  by  a  business  agent  or 

1  Biometrika,  Vol.  VII,  pp.  248-257.  "  On  a  New  Method  of 
determining  Correlation  when  One  Variable  is  given  by  Alternative 
and  the  Other  by  Multiple  Categories." 


10S  Laws  of  Wages 

committee  of  such  organization  acting  under  powers 
conferred  by  the  organization."  Report,  p.  109. 
"  The  strikes  that  are  tabulated  as  not  having  been 
ordered  by  labor  organizations  are  not  necessarily 
strikes  begun  and  carried  on  by  employees  who  were 
not  members  of  an  organization.  They  include  not 
only  this  class  of  strikes,  but  also  strikes  carried  on 
by  members  of  organizations,  when  these  strikes  were 
without  the  authority  of  such  organizations."  Report, 
p.  31. 

The  value  of  77  computed  on  the  assumption  that 
the  alternative  variable  is  normal  in  its  distribution 
is  .218.  The  conclusion  is  therefore  justified  that 
the  results  of  strikes  ordered  by  labor  organizations 
are  more  favorable  to  the  interests  of  laborers  than 
the  results  of  strikes  that  are  not  ordered  by  labor 
organizations.  The  degree  of  association  between 
the  two  variables  is,  however,  rather  low,  and  is 
measured  by  17  =  .218. 

The  second  inquiry  concerning  the  influence 
exerted  by  labor  organizations  on  the  outcome  of 
strikes  may  be  worded  as  follows :  To  what  degree 
is  it  true  that  the  stronger  the  labor  organizations 
in  an  industry,  the  more  favorable  to  the  interests 
of  the  laborers  are  the  results  of  strikes  that  are 
declared  by  labor  organizations  in  the  industry  ? 
In  order  to  obtain  an  answer  to  this  question,  it  will 
be  necessary  to  agree  upon  some  measure  of  strength 
in    labor    organizations,    and   to   array    the   various 


Wages  and  Strikes  109 

industries  of  the  country  in  the  order  in  which  labor 
organizations  are  strong,  in  respect  to  the  quality  of 
strength  that  is  agreed  upon. 

From  one  point  of  view,  the  strength  of  labor 
unions  may  be  measured  by  the  degree  in  which 
the  trade  disputes  in  an  industry  are  ordered  by 
trades-unions.  If  a  large  proportion  of  the  strikes 
in  an  industry  have  their  origin  outside  of  the  trades- 
unions,  it  may  be  assumed,  as  a  general  rule,  not 
only  that  trades-unions  are  not  strong  when  the 
industry  is  considered  as  a  whole,  but  that  the  unions 
in  the  organized  part  of  the  industry  are  not  strong. 
The  fighting  capacity  of  the  organized  part  of  the 
industry  must  be  weakened,  as  a  general  rule,  by 
the  existence  of  a  large  body  of  unorganized  laborers 
in  kindred  occupations  of  the  same  industry. 

When  the  strength  of  trades-unions  is  measured 
by  the  degree  in  which  the  strikes  in  an  industry  are 
ordered  by  trades-unions,  is  there  any  relation  be- 
tween the  strength  of  the  unions  and  the  outcome  of 
strikes  ordered  by  the  unions  ? 

On  pages  33-34  of  the  Report  on  Strikes  am/ 
Lockouts  a  table  is  given  of  "Strikes  and  Establish- 
ments involved  in  Strikes  ordered  by  Labor  Organ- 
izations and  not  so  ordered,  by  Industries,  1881  to 
1905."  This  table  supplies  material  for  ranking  the 
82  enumerated  industries  according  to  the  percent- 
ages of  total  strikes,  in  the  several  industries,  that 
were  ordered  by  labor  organizations.  For  example, 
in  the   industry   for  the  manufacture  of  agricultural 


110  Laws  of  Wages 

implements,  labor  organizations  declared  63.22  per 
cent  of  all  the  strikes  affecting  that  industry  between 
the  years  1881  and  1905  inclusively.  It  is  assumed 
in  the  subsequent  argument  (1)  that  the  control  of 
trade  disputes  of  an  industry  on  the  part  of  labor 
unions  is  proportional  to  the  percentage  of  total 
strikes  affecting  the  industry  that  are  declared  by 
labor  unions;  (2)  that  the  strength  of  the  labor 
organizations  of  a  particular  industry  is  proportional 
to  then-  control  of  trade  disputes. 

On  pages  486-487  of  the  same  Report  there  is 
given  a  table  headed,  "  Summary  of  Strikes  for  the 
United  States,  ordered  by  Labor  Organizations  and 
not  so  ordered,  by  Industries,  1881  to  1905."  The 
same  82  industries  that  appeared  in  the  table  which 
has  just  been  described  are  enumerated  also  in  the 
above  "  Summary."  Furthermore,  this  "  Summary  " 
gives  the  outcome  of  strikes  that  were  ordered  by 
labor  organizations,  according  as  the  strikes  suc- 
ceeded, succeeded  partly,  or  failed. 

From  these  official  data  Table  II  has  been  con- 
structed. The  table  will  afford  the  means  of  meas- 
uring the  relation  between  the  degree  in  which  labor 
unions  control  trade  disputes  and  the  outcome  of 
strikes  ordered  by  unions.  That  is  to  say,  the  table 
will  supply  an  answer  to  the  question  as  to  whether 
the  outcome  of  a  strike  ordered  by  labor  organiza- 
tions is  in  any  way  associated  with  the  measure  in 
which  the  labor  organizations  control  the  trade  dis- 
putes of  the  industry.     If  the  hypothesis  is  accepted 


Wages  and  Strikes 


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112  Laws  of  Wages 

that  the  strength  of  labor  organizations  is  propor- 
tional to  their  control  of  trade  disputes,  Table  II  will 
likewise  supply  an  answer  to  the  question  as  to 
whether  the  strength  of  labor  organizations  has  any- 
thing to  do  with  the  outcome  of  strikes  declared  by 
organizations. 

The  construction  of  the  table  will  be  made  clear 
by  an  illustration.  In  the  first  column  of  the  body 
of  the  table  marked  "  Below  20,"  the  figures  389 
signify  that,  in  all  of  the  industries  covered  by  the 
official  report,  389  establishments  in  which  strikes 
occurred  were  in  industries  in  which  labor  organiza- 
tions declared  below  20  per  cent  of  the  total  strikes 
of  the  industry.  In  case  of  211  of  these  389  estab- 
lishments the  strikes  failed ;  in  67  of  the  establish- 
ments the  strikes  were  compromised  ;  and  in  111  of 
the  establishments  the  strikes  succeeded.  It  will  be 
observed  that  the  table  refers  only  to  the  outcome  of 
strikes  ordered  by  labor  organizations.  All  of  the 
data  in  the  official  summary  have  been  included  ex- 
cept the  material  referring  to  "  domestic  service  "  and 
to  "  miscellaneous." 

From  this  table  two  conclusions  will  be  drawn:  (1) 
as  to  the  nature  of  the  association  between  the  out- 
come of  strikes  and  the  degree  of  control  of  trade 
disputes  on  the  part  of  labor  organizations,  and  (2)  as 
to  the  measure  of  this  relation. 

The  method  employed  in  extracting  the  conclusions 
from  the  data  is  the  method  invented  by  Professor 
Pearson  for  the  derivation  of  the  coefficient  of  mean 


Wages  and  Strikes  L13 

square  contingency.  An  indicatii  in  of  the  significance 
of  the  coefficient  of  mean  square  contingency,  as  a 
measure  of  association,  is  given  hy  the  following  con- 
sideration: The  total  number  of  establishments  in 
which  strikes  occurred  is  seen,  from  the  entry  in  the 
next  to  the  last  column  and  the  bottom  row,  to  have 
been  156,459.  Of  this  total  number  of  establishments 
53,5  12  were  establishments  in  which  the  strikes 
failed;  24,943  were  establishments  in  which  the 
strikes  succeeded  partly  ;  and  78,001  were  establish- 
ments in  which  the  strikes  succeeded.  The  last  column 
marked  "  Chances  "  gives  the  ratio  of  these  numbers, 
respectively,  to  the  total  number  156,459.  If,  now, 
the  outcome  of  the  strikes  in  the  380  establishments 
recorded  in  the  first  column  had  been  similar  to  the 
outcome  in  the  whole  of  the  establishments  enumerated, 
the  number  of  the  establishments  in  which  the  strikes 
failed  would  have  been  (389)  (.3420193)  =  133.05; 
the  number  in  which  strikes  succeeded  partly  would 
have  been  (380)  (.150422)  =  02.02  ;  and  the  number 
in  which  strikes  succeeded  would  have  been  (389) 
(.4985587)  =193.94.  Numbers  derived  in  this  way 
will  be  referred  to  as  the  numbers  given  by  inde- 
pendent probability. 

Now  it  is  clear  that  the  numbers  actually  occurring 
in  the  subgroups  differ  from  those  given  by  inde- 
pendent probability.  In  case  of  the  establishments 
in  which  strikes  failed,  we  have  in  the  first  column 
211-133.05=  +77.05.  And  in  case  of  the  estab- 
lishments in  which  strikes  were  successful,  we  have 


114  Laws  of  Wages 

111  -  193.04  =  -  82.94.  That  is  to  say,  in  industries 
in  which  labor  organizations  were  weakest,  —  in  the 
sense  of  controlling  only  a  small  percentage  of  the 
strikes  that  occurred  in  the  industries,  —  the  outcome 
of  strikes,  in  establishments  in  which  strikes  occurred, 
was  such  that  there  was  a  positive  deviation  from 
independent  probability  of  +77.95  in  case  of  strikes 
that  failed  ;  while,  in  case  of  strikes  that  succeeded, 
there  was  a  negative  deviation  from  independent  prob- 
ability equal  to  —  82.94. 

If,  in  a  similar  manner,  the  column  marked  "  Above 
80  "  is  examined,  it  will  be  found  that,  in  case  of 
establishments  in  which  strikes  failed,  there  is  a  neg- 
ative deviation  equal  to  —  5809.57,  while,  in  establish- 
ments in  which  strikes  succeeded,  there  is  a  positive 
deviation  equal  to  7888.86. 

We  find,  therefore,  that  for  weakly  organized  in- 
dustries, the  successes  are  fewer  and  the  failures  are 
more  than  would  be  given  by  independent  probability  ; 
while  for  strongly  organized  industries  the  contrary 
relation  proves  to  be  true.  These  two  extreme 
columns  suggest  that  the  outcome  of  a  strike  is  in 
some  manner  related  to  the  degree  of  union  control 
of  the  industry,  and  it  is  required  to  determine  rigidly 
from  all  of  the  data  of  the  table  the  quality  and  the 
degree  of  association  between  the  two  variables. 

The  deviations  from  the  independent  probability  of 
the  same  sign,  or  some  function  of  the  deviations  may 
be  taken  as  a  measure  of  the  association.  But,  as  in 
other  forms  of  relation  the  coefficient  of  correlation 


Wages  and  Sir  ikes  115 

has  been  used  to  measure  the  degree  of  association,  it 
is  desirable — in  order  that  types  of  association  like 
that  with  which  we  are  dealing  may  be  compared 
with  types  in  which  the  coefficient  of  correlation  is 
the  appropriate  measure  of  association  —  to  elmox* 
from  the  many  possible  functions  of  deviations  from 
independent  probability  such  a  function  that,  in  ease  of 
normal  distribution  where  the  two  methods  may  be 
applied,  the  measure  of  association  remains  the  same, 
whether  it  is  computed  by  the  newer  method  or  by  the 
method  of  the  coefficient  of  correlation.  The  coeffi- 
cient of  mean  square  contingency,  which  is  a  function 
of  the  squares  of  the  deviations  from  independent 
probability,  and  the  coefficient  of  mean  contingency, 
which  is  a  function  of  the  deviations  of  the  same  sign, 
are  two  functions  that  fulfill  the  above  conditions. 
If  the  former  coefficient  be  represented  by  C,  and  the 
latter  by  C2,  then,  in  case  of  normal  distribution  when 
all  three  methods  may  be  applied,  C{  =  C.,  =  r,  where  r 
is  the  coefficient  of  correlation.  The  range  of  value 
of  Cx  and  C2  is  from  zero  to  unity.  Their  signs  must 
be  determined  by  special  methods.1 

When  the  association  or  contingency  between  the 
degree  of  union  control  of  strikes  and  the  outcome  of 
strikes  is  computed  from  our  Table  II  by  means  of 
the  contingency  coefficients,  we  obtain  for  the  coeffi- 
cient of  mean  square  contingency  C{  =  .232 ;  and 
for  the  coefficient  of  contingency  C,  =  .30. 

1  Karl  Pearson  :  On  The  Theory  of  Contingency  and  its  Relation 
to  Association  and  Normal  Correlation. 


116  Laws  of  Wages 

The  conclusions  from  the  investigation  are,  there- 
fore: (1)  The  greater  the  degree  in  which  labor 
organizations  control  the  disputes  of  an  industry,  the 
more  likely  is  the  outcome  of  a  strike  declared  by 
labor  organizations  to  be  favorable  to  the  interests  of 
laborers  ;  (2)  The  measure  of  the  association  between 
the  degree  in  which  labor  unions  control  trade  disputes 
and  the  outcome  of  strikes  declared  by  organizations 
is  C{  =  .232  and  C,  =  .30. 

Figure  15  illustrates  the  association  between  the 
two  variables.  The  diagram  is  constructed  on  the 
assumption  that  the  variable  which  measures  the  out- 
come of  strikes  is  distributed  according  to  the  normal 
law.1  The  origin  is  taken  at  a  line  separating  estab- 
lishments in  which  strikes  "  succeeded  partly  "  from 
establishments  in  which  strikes  "  failed."  The  zig- 
zag line  is  the  line  of  the  means  of  the  respective  cate- 
gories. It  is  seen  that  the  mean  outcome  of  strikes,  in 
industries  in  which  below  20  per  cent  of  the  strikes  were 
called  by  labor  organizations,  was  a  failure  ;  while  in 
industries  in  which  above  80  per  cent  of  the  strikes 
were  called  by  labor  organizations,  the  mean  outcome 
of  strikes  was  a  success.  As  the  degree  of  control  of 
trade  disputes  by  labor  organizations  increases,  the 
general  trend  of  the  mean  outcome  of  strikes  moves 
from  failure,  through  compromise,  to  success. 

There  is  need  of  great  caution  in  the  interpretation 

1  Let  it  be  observed  that  no  point  in  the  argument  is  dependent 
iipnu  litis  assumption.  This  form  of  diagram  was  invented,  I  believe, 
by  Professor  Pearson. 


U'dfjes  and  Strikes 


117 


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=5 
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118  Lcucs  of  Wages 

of  these  results.  It  is  not  to  be  inferred  that  the 
relation  between  the  strength  of  labor  unions  and  the 
outcome  of  strikes  is  a  relation  of  cause  and  effect. 
The  low  value  of  Cx  precludes  the  hypothesis  of  a 
direct  cause  and  effect  relation.  The  two  phenomena 
may  be  joint  effects  of  a  common  cause.  Moreover, 
the  results  have  been  determined  from  data  as  to  all 
industries  and  as  to  all  causes.  The  mixing  of  the 
material  in  this  manner  introduces  an  element  into 
the  problem  the  influence  of  which  it  would  be  dif- 
ficult to  measure.  Suppose  that  the  outcome  of  strikes 
is  dependent  upon  the  nature  of  the  particular  causes 
for  which  the  strikes  are  called,  that  is  to  say,  suppose 
that  the  probabilities  of  the  outcome  of  strikes  being 
in  favor  of  the  laborers  vary  according  to  the  nature 
of  the  causes.  Then,  if  labor  organizations  in  weakly 
organized  industries  are  predisposed  to  strike  for 
causes  that  are  likely  to  fail,  while  the  stronger  unions 
enter  into  trade  disputes  for  more  promising  causes, 
the  results  that  we  have  obtained  would  find  their 
explanation  not  in  the  degree  in  which  labor  unions 
control  trade  disputes,  but  in  the  wisdom  with  which 
strong  unions  choose  the  grounds  of  the  disputes  into 
which  they  enter. 

Before  taking  up  these  considerations,  we  may  note 
another  relation  that  has  a  bearing  upon  the  outcome 
of  strikes,  as  far  as  the  outcome  is  affected  by  the 
strength  of  labor  organizations.  Is  the  result  of  a 
strike  the  more  likely  to  be  favorable  to  the  interest 
of  the  laborers,  the   greater  the  length  of  time  the 


Wages  and  Strikes 


11'.) 


laborers  hold  out  ?  Or  is  the  contrary  the  case  ?  If 
the  duration  of  a  strike  and  its  outcome  are  either 
directly  or  inversely  related,  what  is  the  measure  of 
the  degree  of  association  between  the  two? 


TABLE  III.  —  Contingency  betwken  the  Dukation  of  Strikes 
and  the  Outcome  oe  Strikes.     Germany,    L899   1905 


LtWi,   "I     DUBATIO.N 

Toi  u 

1-5 

6  10 

11-20 

•21-30 

31-50 

51-100 

101  or 
over 

< 

P 
00 

s 

/. 

:*. 
Z 

H 

a 

S3 

Succeeded 

1134 

353 

275 

122 

80 

57 

14 

2035 

Succeeded 
partly 

1106 

601 

577 

:;i;i 

336 

299 

124 

3407 

Failed 

1563 

598 

517 

344 

434 

438 

181 

1075 

Total 

3803 

1552 

1369 

830 

850 

794 

319 

9517 

TABLE  TV. — Contingency  between  the  Dukation  of  Strikes 
and  the  Outcome  of  Strikes.     France  1890-1905 


Days  in    Duration 

Total 

7  or 

under 

8-15 

16-30 

31-100 

101  or 
over 

< 

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CO 
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285 

132 

98 

4 

2041 

Succeeded 
partly 

1665 

618 

379 

328 

36 

3026 

Failed 

2131 

613 

337 

337 

51 

3469 

Total 

5318 

1 

1516 

848 

763 

91 

8536 

120  Laws  of  Wages 

Tables x  III  and  IV,  referring  respectively  to  the 
history  of  strikes  in  Germany  from  1899  to  1905,  and 
to  the  history  of  strikes  in  France  from  1890  to  1905, 
supply  material  for  answering  these  questions.  In 
case  of  the  figures  for  Germany  C1  —  .22;  C2  =  .26.  In 
case  of  the  figures  for  France,  C{  =  .16;  C,  =  .19. 

It  may  be  concluded  that  — 

(1)  the  greater  the  duration  of  the  strike,  the  less 

likely  is  the  outcome  of  the  strike  to  be  favor- 
able to  the  interests  of  the  laborers ; 

(2)  the  measure  of   the  association    between    the 

duration  of  strikes  and  the  outcome  of  strikes 
is,  in  case  of  Germany,  Cx  =  .22  ;  in  cas'e 
of  France,  (7,  =  .16. 

Here  again  caution  in  the  interpretation  of  the 
results  is  very  necessary.  Is  it  to  be  inferred  from 
the  above  conclusions  that  protracted  strikes  tend  to 
end  contrary  to  the  interests  of  laborers  because  the 
greater  duration  of  the  struggle  exhausts  the  funds 
of  trades-unions  and  weakens  their  fighting  capacity  ? 
The  inference  is  not  warranted  by  the  data.  The 
low  coefficients  of  contingency  suggest  the  unwisdom 
of  drawing  any  conclusion  from  the  data  as  to  cause 
and  effect.  Besides,  the  lumping  of  the  results  of  all 
causes  of  strikes  leaves  room  for  an  indefinite  number 
of  hypotheses  as  to  the  specific  cause  of  the  relation 
that  has  been  established.     May  it  not  be  true  that 

1  The  tables  are  taken  from  the  Report  for  1906  on  Strikes  and  Lock- 
outs, pp.  859,  840. 


Wages  and  Strikes  \2\ 

strong  unions,  when  they  do  enter  into  trade  disputes, 
strike  for  causes  that  are  likely  to  end  quickly  in  the 
interests  of  the  laborers,  while  the  weaker  unions  vainly 
protract  their  disputes  through  ignoring  economic 
laws  in  the  choice  of  the  time  and  grounds  of  their 
strikes  ? 

Outcome  of  Strikes  as  Limited  by  Economic  Law. 

This  discussion  brings  us  to  the  consideration  of 
the  role  of  economic  law  in  determining  the  out- 
come of  strikes.  In  searching  for  the  influence  of 
economic  laws  in  this  particular  field  the  first  ques- 
tion that  one  is  led  to  ask  takes  this  form :  Is  the 
outcome  of  a  strike,  so  far  as  the  interests  of  the 
laborers  are  concerned,  independent  of  the  nature 
of  the  cause  of  the  strike  ?  This  question  may 
be  put  more  concretely.  The  Bureau  of  Labor  of 
the  United  States  classifies  strikes  according  as  they 
had  their  origin  in  one  or  more  of  fourteen  causes. 
Is  it  found,  from  the  record  of  the  Bureau,  that 
strikes  succeed,  succeed  partly,  or  fail  in  the  same 
proportion  of  cases,  no  matter  what  the  cause  of 
the  strikes  may  be  ?  Or  is  it  true  that  certain 
causes  of  strikes  are  more  likely  to  lead  to  success- 
ful issues  than  other  causes?  The  answering;  of 
these  questions  will  put  one  in  the  way  of  con- 
necting the  outcome  of  strikes  with  economic  causes. 

Table  V,  which  was  compiled  from  the  Report  on 
Strikes  and  Lockouts,  p.  63,  makes  possible  the 
computation  of  the  contingency  between  the  causes 


122 


Laws  of  Wages 


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SaHIHXq  .1"  :u«."  uno 

Wages  and  Sir  ikes  L23 

of  strikes  and  the  outcome  of  strikes.  The  table 
includes  the  results  only  of  strikes  that  were  under- 
taken for  single  causes;  it  does  not  deal  with  the 
results  of  strikes  in  which  the  causes  were  mixed. 

The  computation  of  the  contingency  coefficients 
gives  CL  =  .298  ;  C,  =  .33.  With  these  values  defi- 
nitely ascertained,  it  cannot  be  denied  that  the  out- 
come of  a  strike  is  associated  with  the  kind  of  cause 
for  which  the  strike  is  undertaken. 

From  Table  V,  it  is  also  possible  to  derive  values 
that  will  throw  light  upon  the  ranking  of  causes 
according  as  they  are  the  origin  of  strikes  that  are 
likely  to  succeed,  to  succeed  partly,  or  to  fail.  If 
the  percentage  deviations  of  the  actual  figures  in  the 
subcontingency  groups  are  computed  from  independ- 
ent probability,  then  the  magnitudes  and  signs  of 
the  percentages  will  supply  indices  of  the  rank  of 
the  causes.  For  example,  in  case  of  the  group  in 
the  upper  left-hand  corner,  the  actual  frequency  is 
30,142,  the  theoretical  frequency  given  by  independ- 
ent   probability    is    28,360;    the   relative   deviation 

is  therefore  3014o2",2n8860  =  +  .0028.     For  the  sub- 

group    in    the  upper   right-hand  corner  the    relative 

deviation    is    131^~  f 88  =  -  -5599.      In    the    first 

ease,  that  is  to  say,  in  case  of  strikes  for  an  increase 
of  wages,  there  is  a  positive  deviation  of  the  success- 
ful strikes  equal  to  6.28  per  cent,  while  in  case  of 
sympathetic  strikes,  there  is  a  negative  deviation 
of  55.99  per  cent. 


124 


Laws  of  T rages 


TABLE  VI.  — The  Rank  of  Causes  of  Strikes  according  as 
Strikes  undertaken  for  the  Particular  Causes  devi- 
ated, in  their   Outcome,  from    Independent   Probability 


Succeeded 

Succeeded  Partly 

Failed 

(1)  Concerning  recog- 

(1) For  increase  of 

(1)  In  sympathy 

nition  of  the  union 

wages. 

with  strikers 

and  union  rules. 

elsewhere. 

(2)  For  reduction  of 

(2)  Against  increase 

(2)  Concerning  em- 

hours. 

of  hours. 

ployment  of  cer- 
tain persons. 

(3)  Against  increase 

(3)  Against  reduction 

(3)  Concerning 

of  hours. 

of  wages. 

working  rules 
and  conditions. 

(4)  For  increase  of 

(4)  For  reduction  of 

(4)  Against  reduc- 

wages. 

hours. 

tion  of  wages. 

(5)  Concerning  work- 

(5) Concerning  work- 

(5) Concerning  rec- 

ing conditions  and 

ing  conditions  and 

ognition  of  union 

rules. 

rules. 

and  union  rules. 

(G)  Against  reduction 

(6)  In  sympathy  with 

(G)  For  reduction 

of  wages. 

strikers  elsewhere. 

of  hours. 

(7)  Concerning  em- 

(7) Concerning  em- 

(7) Against  increase 

ployment  of  cer- 

ployment of  cer- 

of hours. 

tain  persons. 

tain  persons. 

(8)  In  sympathy  with 

(8)  Concerning  recog- 

(8) For  increase  of 

strikers  elsewhere. 

nition  of  union 
and  union  rules. 

wages. 

In  Table  VI,  the  causes  of  strikes  are  ranked 
according  as  strikes  undertaken  for  the  particular 
causes  deviate,  in  their  outcome,  from  independent 
probability.  It  is  found,  for  instance,  that  a  strike 
for  the  recognition  of  the  union  has  been  the  most 
likely  to  succeed ;  a  strike  for  an  increase  of  wages 
has  been  the  most  likely  to  be  compromised ;  and 
a    strike    in    sympathy  with  workers  elsewhere  has 


Wages  and  Strikes 


L25 


been  the  most  likely  to  fail.     The  other  causes  rank 
in  the  order  of  their  sequence  in  the  table. 

An  examination  of  Table  V  also  discloses  that, 
dining  the  period  covered  by  the  Report,  the  most 
important  causes  of  strikes  were  "  For  an  increase 
of  wages  "  and  "  Concerning  recognition  of  the  union 
and  union  rules."  These  two  causes  of  strikes,  to 
which  were  due  more  than  50  per  cent  of  all  the 
strikes  that  occurred  between  1881  and  1905,  will 
be  subjected  to  further  treatment. 

TABLE  VII.  — Percentages  of  Total  Strikes  that  were 
called,  respectively,  for  an  [ncrease  of  wages  and 
for  the  Recognition  of  the  Union  and  Union  Rules 


Tear 

For  an 
Increase  of 

\\   LGES 

(  lONCERNING 

the  Recogni- 
tion  OF  THE 

I'M*  >N    AND 

Union  Rules 

Year 

For  an 

Increase  of 

Wages 

Concerning 
the  Recogni- 
tion of  Tin: 

UNION      \\|. 

Union  Rules 

1881 

61.15 

5.73 

1894 

30.5  1 

12.45 

1882 

54.41 

5.95 

1895 

41.98 

12.35 

1883 

45.40 

7.53 

1896 

26.80 

21.93 

1884 

29.57 

6.77 

1897 

35.81 

12.99 

1885 

37.52 

7.11 

1898 

36.36 

15.72 

1886 

41.69 

8.73 

1899 

38.8  1 

19.53 

1887 

33.64 

15.60 

1900 

32.94 

L5.35 

1888 

25.94 

13.69 

1901 

29.04 

27.  !»S 

1889 

29.95 

12.65 

1902 

32.86 

25.27 

1890 

31.48 

12.88 

1903 

31.57 

23.24 

1891 

26.67 

14.27 

1904 

23.19 

32.42 

1892 

29.12 

15.25 

1905 

28.07 

30.86 

1893 

24.21 

13.72 

Table  VII,  which  was  taken  from  the  volume  on 
Strikes  and  Lockouts,  1906,  p.  56,  gives  the  per- 
centages of  total  strikes  that    were    undertaken  for 


126 


Laws  of  Wages 


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Wages  and  Strikes  1-7 

these  two  causes  between  the  years  1881—1905,  in- 
clusively. When  these  figures  arc  plotted,  as  in 
Figure  16,  it  is  observed  that  the  general  trend  of 
the  percentage  of  strikes  undertaken  for  an  increase 
of  wages  has  been  downward,  while  the  general 
trend  of  the  percentage  of  strikes  for  a  recognition 
of  the  union  rules  has  been  upward.  Furthermore, 
there  is  an  inverse  correlation  between  the  deviations 
in  the  two  cases,  that  is  to  say,  when  the  percentage 
of  strikes  for  an  increase  of  wages  rises  above  the 
general  trend,  the  percentage  of  strikes  for  a  recog- 
nition of  the  union  tends  to  fall  below  the  general 
trend  and  vice  versa.  The  coefficient  of  correlation 
between  these  deviations  from  the  general  trend  is1 
r  =  -  .228. 

An  additional  light  upon  this  very  same  question 
of  the  relation  of  these  two  causes  is  afforded  by 
Table  VI 1 1,  which  is  taken  from  the  same  Report 
on  Strikes  and  Lockouts,  p.  622.  The  table  gives 
the  percentages  of  total  strikes  that  were  successful 
when  the  causes  of  the  strikes  were,  respectively, 
for  an  increase  of  wages  and  for  a  recognition  of 
the  union.  The  general  trend  —  Figure  17  —  of  the 
percentages  of  total  strikes  that  were  successful  was 
downward,  in  case  of  strikes  for  an  increase  of  wages, 

1  No  argument  is  dependent  upon  the  absolute  value  of  this 
coefficient.     It  contains  a  spurious  element. 

Th ruation  to  the  general  trend,  for  the  percentages  of  total 

strikes  that  were  called  for  an  increase  of  wages,  is  y  =34.43  —  .6466  x  : 
and  for  the  percentages  called  for  a  recognition  of  the  union, 
y  =  15. 57  +  . 8967  x,  the  origin  in  both  cases  being  in  the  middle  of  the 
year  1893. 


128 


Laws  of  Wages 


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Wages  and  Strikes 


L29 


and  upward,  in  case  of  strikes  for  a  recognition 
of  the  union.  Moreover,  the  percentage  deviations 
from  the  general  trend1  in  case  of  successful  strikes 
for  the  recognition  of  the  union  were  inversely  corre- 
lated with  the  percentage  deviations  from  the  gen- 
eral trend  in  case  of  successful  strikes  for  an  increase 
of  wages.     The  coefficient  of  correlation  is  r=  —  .207. 

TABLE  Vlir.  —  Pkrcentage  of  Strikes  that  were  success- 
ful when  the  Causes  of  the  Strikes  were,  respectively, 
fob  an  Increase  of  Wages  and  concerning  the  Recog- 
nition of  the  Union  and  Union  Rules 


Year 

For  an 
Increase  of 

Wages 

Concerning 
tiik  Recogni- 
tion ok  THE 
Union  and 
Union  Rules 

Tear 

For  an 

Increase  of 

Wages 

Concerning 

tiik    Re M 

HON    OF    THE 

Union  and 
Union  Rules 

1881 

73.02 

40.74 

1894 

31.04 

75.84 

1882 

56.86 

50.00 

1895 

37.11 

71.19 

1883 

74.31 

17.50 

1896 

62.15 

68.78 

1884 

57.25 

30.00 

1897 

40.92 

92.17 

1885 

61.13 

50.7.") 

1898 

60.00 

87.67 

1S86 

00.44 

40.58 

1899 

53.06 

62.43 

1887 

4S.97 

53.41 

1900 

37.60 

31.06 

1888 

63.53 

47.04 

1901 

53.92 

57.26 

1889 

53.45 

46.85 

1902 

56.29 

55.14 

1890 

45.64 

45.25 

1903 

46.98 

66.48 

1891 

37.01 

69.46 

1904 

39.22 

36.60 

1892 

55.01 

13.09 

1905 

45.73 

43.83 

1893 

47.39 

82.01 

Thus  far  it  has  been  possible  to  establish  that 
strikes  for  an  increase  of  wages  decreased  in  relative 

1  The  equation  to  the  general  trend  of  the  successful  strikes  for  an 
increase  of  wages  is  y  —  52. 45  —  .8014  x;  and  for  the  recognition  of  the 
union,  y =53. 55+. 9848 x,  the  origin  in  both  cases  being  in  the  middle 
of  the  year  1893. 


130  Laws  of  Wages 

importance  in  the  interval  1881-1905;  that  the  per- 
centage of  successful  strikes  for  an  increase  of  wages 
decreased  during  the  same  period ;  that  during  the 
same  epoch  there  was  an  increase  in  the  relative 
number  of  strikes  for  the  recognition  of  the  union  and 
an  increase  in  the  percentage  of  successful  strikes  for 
the  recognition  of  the  union.  Furthermore,  it  has 
been  established  that  the  percentage  deviations  from 
the  general  trend  are  inversely  correlated  both  in  case 
of  the  relative  importance  of  the  two  causes  of  strikes 
and  in  case  of  the  percentage  of  successful  strikes  due 
to  the  two  causes. 

In  view  of  the  dominant  importance  of  these  two 
causes  of  strikes  and  of  their  interrelation,  it  is  clear 
that  if  the  outcome  of  strikes  for  either  cause  could 
be  shown  to  be  dependent  upon  economic  law,  a  large 
part  of  the  theory  of  strikes  would  be  brought  into 
intimate  and  real  relation  with  the  general  theory  of 
distribution. 

Table  IX  has  been  compiled  from  the  data  contained 
in  M.  Francois  Simiand's  work  :  Le  Salaire  des  ouvriers 
des  mines  de  charbon  en  France.  On  pages  351-365 
of  that  work  M.  Simiand  has  given  the  results  of 
strikes  relative  to  wages  and  conditions  of  work  in 
the  coal  mining  districts  of  the  basins  of  Loire,  Nord, 
and  Pas-de- Calais.  I  have  computed,  for  these  three 
districts,  in  Chapter  III,  on  "  Wages  and  the  Produc- 
tivity of  Labor,"  the  equation  to  the  general  trend  of 
the  ratio  of  wages  to  the  value  of  the  product  per 
laborer  per  day,  and  I  have    given  the   percentage 


\\'<iyes  and  Strikes 


i::i 


deviations  of  these  ratios,  for  each  year,  from  the  gen- 
eral trend,  during  the  period  1848-1901.  By  means 
of  these  two  bodies  of  results  Table  IX  has  been  con- 
structed. The  112  strikes  recorded  by  M.  Simiand 
have  been  classified  according  as  they  fall  into  the 
sixteen  subcontingency  groups  of  the  table. 

TABLE   IX.— Contingency  between  the  Rate  of  Wages 
and  the  Outcome  of  Strikes 


Percentage  Deviation  of  Wages  from 
the  General  Trend 

Total 

Above  +4 

0  to  +4 

ii  to  -4 

Below  —  4 

H 

■£ 

3 
/: 

o 

© 

- 

- 
Z 

Successful 

3 

5 

12 

7 

27 

Very  Favorably 
and  Favorably 

Compromised 

1 

5 

1 

7 

Compromised 

6 

1 

11 

2 

20 

Failed 

18 

10 

26 

4 

58 

Total 

27 

17 

54 

11 

112 

When  the  coefficients  of  contingency  are  computed, 
it  is  found  that  C,  =  .327  and  C.,=  between  .36  and 
.37.     The  conclusions  are — 

(1)  The  outcome  of  strikes  for  the  causes  affect- 
ing  wages  or    the    conditions    of    work    is 


132  Laics  of  Wages 

related  to  the  deviations  from  the  general 
trend  of  the  ratio  of  wages  to  the  value 
of  the  product,  that  is  to  say,  the  outcome  of 
strikes  affecting  wages  and  the  conditions  of 
work  is  likely  to  be  favorable  or  unfavorable 
to  the  interests  of  the  laborers  according  as 
the  prevailing  share  of  the  laborer  in  the  value 
of  the  product  is  below  or  above  the  general 
trend  of  that  share  ; 
(2)  The  measure  of  this  relation  is  C^.327; 
(72=.36-.37. 

But  the  above  coefficients  relate  to  M.  Simiand's 
entire  number  of  strikes  between  the  years  1848-1901. 
The  causes  of  the  tabulated  strikes  were,  however, 
mixed  causes.  M.  Simiand  has  included  all  causes 
affecting  wages  and  conditions  of  work,  and  conse- 
quently such  causes  find  their  place  in  his  table  as 
payment  for  supplies,  hours  of  work,  employment  of 
foreigners,  conduct  of  overseers,  and  dismissal  of  work- 
men. But  we  have  established  that  the  outcome  of 
strikes  varies  according  to  the  causes  of  strikes,  and 
therefore  it  is  desirable  to  narrow  the  investigation 
and  to  inquire  whether  there  is  any  relation  between 
the  rate  of  wages  and  the  outcome  of  strikes  for  an 
increase  of  wages. 

Table  X  has  been  compiled  from  M.  Simiand's  data 
by  including  only  those  strikes  that  had  their  origin 
in  a  demand  for  an  increase  of  wages.  The  material 
has  been  treated  by  the  Pearsonian  method  for  evalu- 


Wages  and  Strikes 


133 


ating  the  correlation  ratio  when  one  variable  is  given 
by  alternative  categories  and  the  other  by  multiple 
categories.  The  percentage  deviations  from  the  gen- 
eral trend  of  the  ratio  of  wages  to  the  value  of  the 
product  per  laborer  have  been  assumed  to  conform  to 
the  normal  law. 


TABLE   X.  — Correlation  between  the  Rate  of  Wages  and 
the  Outcome  of  Strikes  for  an  Inckkase  of  Wages 


Outcome  of  Strikes 

Total 

Succeeded 
Partly 

Failed 

eft 

- 
-J 

Above  general  trend 

3 

1 

10 

11 

Below  general  trend 

8 

6 

11 

•_>:» 

Total 

11 

21 

39 

The  value  of  the  correlation  ratio  is  77  =  .370,  which 
is  the  highest  degree  of  relation  that  we  have  found 
in  this  chapter.  The  conclusions  are  (1)  that  the  out- 
come of  strikes  for  an  increase  of  wages  is  related  to 
the  deviations  from  the  general  trend  of  the  ratio  of 
wages  to  the  value  of  the  product  per  laborer ;  (2)  the 
degree  of  the  relation  is  measured  by  77  =  .370.  The 
outcome  of  a  strike  for  an  increase  of  wages  is  likely 
to  be  favorable  to  the  interests  of  the  laborers  when 
the  ratio  of  wages  to  the  value  of  the  product  per 
laborer  is  below  the  general  trend  of  that  ratio.  The 
outcome  is  likely  to  be  adverse  to  the  interests  of  the 
laborers  when  the  prevailing  ratio  is  above  the  general 


13-4  Laws  of  Wages 

trend.  The  general  trend  itself,  as  we  discovered  in 
the  chapter  on  "  Wages  and  the  Productivity  of 
Labor,"  is  conditioned  by  the  degree  and  nature  of  the 
organization  of  capital  and  labor  in  production. 

Summary. 

In  beginning  this  chapter  it  was  assumed  that  both 
labor  organizations  and  economic  law  affect  the  out- 
come of  trade  disputes  as  to  wages,  and  the  scientific 
task  that  was  imposed  was  to  measure,  as  far  as 
possible  with  available  data,  the  relative  importance 
of  the  two  factors  in  the  determination  of  the  result- 
ing rate  of  wages.  The  conclusions  of  the  investiga- 
tion may  be  summarized  under  two  headings ;  (A) 
The  influence  of  labor  organizations ;  (B)  The 
influence  of  economic  law. 

(A)  The  influence  of  labor  organizations. 

(1)  The    results    of    strikes    ordered    by   labor 

organizations  are  more  favorable  to  the 
interests  of  the  laborers  than  the  results  of 
strikes  that  are  not  ordered  by  labor  or- 
ganizations. The  measure  of  association 
between  the  outcome  of  strikes  and  the 
calling  or  not  calling  of  strikes  by  labor 
organizations  is  given  by  77  =  .218. 

(2)  The  greater  the  degree  in  which  labor  organ- 

izations control  the  trade  disputes  of  an 
industry,  the  more  likely  is  the  outcome  of 
a  strike  declared  by  labor  organizations  to 
be  favorable  to  the  interests  of  laborers. 


Wages  and  S  tri Ices  L35 

The  measure  of  association   between  the 
degree  in  which  labor  organizations  control 

trade  disputes  and  the  outcome  of  strikes 
declared  by  labor  organizations  is  given  by 

(3)  The  greater  the  duration  of  a  strike,  the  less 
likely  is  its  outcome  to  be  favorable  to  the 
interests  of  the  laborers.  The  measure  of 
association  between  the  duration  of  strikes 
and  the  nature  of  the  outcome  of  strikes  is 
d=  .22  in  case  of  Germany,  and  C{  =  .16 
in  case  of  France. 
(B)  The  influence  of  economic  law. 

The  relations  summarized  under  (A)  must  not  be 
assumed  to  be  relations  of  cause  and  effect. 
The  low  coefficients   measuring   the   degrees 
of  association   preclude  any  inference  as   to 
causal  relations.     Moreover,  the  results  are 
ao-oreo-ate  results  of  mixed  causes  and  mixed 
conditions.     A  complete  investigation  would 
require  a  segregation  of  the  material  and  its 
treatment   according  to  differing   conditions 
and  causes.     The  results  of  this  preliminary 
study,  which  goes  as  far  in  the  direction  of  seg- 
regation of  materials  as  the  present  sources 
will  admit,  are  as  follows:  — 
(1)  The  outcome  of  strikes  is  associated  with  the 
kinds  of  causes  for  which  strikes  are  un- 
dertaken.    The  coefficient  measuring  the 
degree  of  association  is  Cx  =  .298. 


136  Laws  of  Wages 

(2)  The  causes  of  strikes  may  be  ranked  accord- 

ing as  they  have  been  the  origin  of  strikes 
that  succeeded,  succeeded  partly,  or  failed. 

(3)  The  most  important  causes  of  strikes  have 

been  "  for  an  increase  of  wages  "  and  "  for 
the  recognition  of  the  union  and  union 
rules." 

(a)  The  general  trend  of  the  ratio  of  strikes 
"for  an  increase  of  wages"  to  total 
strikes  has  been  downward  ;  the  gen- 
eral trend  of  the  ratio  of  strikes  "  for 
the  recognition  of  the  union  "  to  total 
strikes  has  been  upward. 

(6)  The  general  trend  of  the  ratio  of  success- 
ful strikes  "  for  an  increase  of  wages" 
to  total  strikes  "  for  an  increase  of 
wages"  has  been  downward;  the  gen- 
eral trend  of  the  ratio  of  successful 
strikes  "  for  the  recognition  of  the 
union"  to  total  strikes  "for  the 
recognition  of  the  union"  has  been 
upward. 

(c)  There  is  an  inverse  correlation  between 
the  percentage  deviations  from  the 
general  trend  of  the  ratio  of  strikes 
"  for  an  increase  of  wages '  to  total 
strikes,  and  the  percentage  deviations 
from  the  general  trend  of  the  ratio 
of  strikes  "  for  the  recognition  of 
the  union  "  to  total  strikes. 


Wages  and  Strikes  137 

(V)  There  is  an  inverse  correlation  between 
the    percentage   deviations    from    the 
general  trend  of  the  ratio  of  successful 
strikes  "for  an  increase  of  wages"  to 
total  strikes  "for  an  increase  of  wages," 
and  the  percentage    deviations   from 
the  general  trend  of  the  ratio  of  suc- 
cessful strikes  "  for  the  recognition  of 
the  union  "  to  the  total  strikes  "  for 
the  recognition  of  the  union." 
This  intimate  connection  of  the  two  most 
important  causes  of  strikes  led  to  the 
attempt  to  connect  one  of  the  causes 
with    the   economic    laws   that   have 
been  established  in  a  preceding  chap- 
ter.    It  was  found  that  — 
(4)  The   results  of   strikes    for   general   causes 
affecting  wages  and   conditions  of   work 
are  associated  with  the  percentage  devia- 
tions of  the  laborer's  share  of  the  product 
from  the  general  trend  of  that  share.     The 
outcome  of   a    strike  for   general    causes 
affecting  wages  and    conditions  of   work 
is  likely  to  be  favorable  to  the  interests 
of  the  laborers  when  the  laborer's  share  in 
the  product  of  industry  is  below  the  gen- 
eral trend  of  that   share.     The  outcome 
of   the   strike  is  likely  to  be  adverse   to 
the    interests    of   the   laborers    when    the 
laborer's  share  is  above  the  general  trend. 


138  Laws  of  Wages 

The  coefficient  measuring  the  association 
is  Cx  =  .327. 
(5)  The  outcome  of  a  strike  "  for  an  increase  of 
wages  "  is  related  to  the  percentage  devia- 
tion of  the  laborer's  share  of  the  product 
from  the  general  trend  of  that  share.  The 
result  is  likely  to  be  favorable  if  the  la- 
borer's share  is  below  the  general  trend  ;  it 
is  likely  to  be  adverse,  in  the  contrary  case. 
The  measure  of  the  relation  is  rj  =  .370. 
This  last  coefficient  is  based  upon  a  small  num- 
ber of  cases  and  consequently  the  probable 
error  is  high.  From  the  nature  of  the  data 
examined  there  is  reason  for  supposing 
that,  with  a  larger  number  of  cases,  the 
correlation  ratio  would  be  much  higher. 


CHAPTER   VI 

WAGES   AND   THE   CONCENTRATION   OF   INDUSTRY 

"  II  mettere  in  luce  1'  influenza  dell'  impresa  e  dell' eta  dell'  operaia 

Bull'  altezza  dei  salari,  ci  sembra  ricerca  della  maggiore  importauza 

teorica  e  pratica." 

—  La  Donna  NelU  Industrie*  Ttaliana,  p.  ix. 

The  investigation  upon  which  we  are  about  to  enter 
as  to  the  influence  upon  the  status  of  the  laborer  of 
the  concentration  of  industry  in  large  establishments 
is  of  both  theoretical  and  practical  importance.  Its 
practical  value  lies  in  the  answer  to  the  question  as 
to  whether  the  form  of  selection  of  laborers  entailed 
by  the  survival  in  competition  of  large  establishments 
places  the  employees  upon  a  better  plane  of  living 
than  the  one  occupied  by  their  fellow-workers  in 
smaller  establishments.  Its  theoretical  interest  lies 
in  the  answer  to  the  query  as  to  whether  the  pro- 
ductivity hypothesis  will  explain  the  results  to  which 
the  investigation  will  lead. 

We  shall  approach  our  problem  by  considering  the 
relation  of  the  size  of  the  establishment  (1)  to  the 
rate  of  wages,  (2)  to  the  amount  of  employment, 
(3)  to  the  continuity  of  employment,  and  (4)  to  the 
length  of  the  working  day. 

Because  of  the  complexity  of  the  undertaking, 
there  is  great  likelihood   of    obtaining    spurious   re- 

13!> 


140  Laws  of  Wages 

suits  in  consequence  of  the  mixing  of  heterogeneous 
data.  The  following  cautions  should  be  observed  as 
far  as  possible  in  selecting  material  upon  which  to 
base  the  investigation:  Data  should  be  segregated 
(1)  referring  to  different  sexes;  (2)  referring  to  la- 
borers of  different  ages  ;  (3)  according  as  the  data  are 
drawn  from  different  geographical  districts ;  (4)  ac- 
cording as  they  are  drawn  from  city  and  country; 
(5)  referring  to  industries  bearing  the  same  generic 
name  but  producing  different  commodities.  Unfor- 
tunately, statistics  appropriate  to  the  solution  of  dif- 
ficult economic  problems  cannot  be  had  for  the  ask- 
ing, so  that,  in  the  treatment  of  several  points  in  this 
chapter,  I  have  been  compelled  to  use  data  that  do 
not  in  all  respects  fulfill  ideal  requirements. 

Wages  as  Affected  by  the  Concentration  of  Industry. 

The  first  three  tables  in  the  Appendix  to  this  chap- 
ter refer  to  the  daily  wages  of  women,  above  fifteen 
years  of  age,  employed  in  the  manufacture  of  textiles 
in  Italy.1 

We  obtain, 

(1)  from  Table  I,  the  coefficient  of  mean  square 
contingency  between  the  size  of  the  estab- 
lishment and  the  rate  of  wages, 

^=.318; 

1  The  tables  in  this  chapter  that  present  Italian  data  are  drawn 
from  the  publication  of  the  Ufficio  del  Lavoro :  La  Donna  NeW  Indus- 
trial Italiana,  Roma,  1905. 


Wiiiji's  (ind  the  Concentration  of  Industry      141 

(2)  from  Table  II.  the  coefficient  of  mean  squan- 

contingency  between  the  rate  of  wages  and 
the  age  of  the  worker, 

(3)  from  Table  III,  the  coefficient  of  mean  square 

contingency  between  the  age  of  the  laborer 
and  the  size  of  the  establishment, 

^  =  .06. 

With  these  crude  coefficients  of  contingency,  it 
would  be  possible  to  evaluate,  by  the  method  of  mul- 
tiple contingency,  the  net  relation  between  wages 
and  the  size  of  the  establishment.  But  such  a  net 
coefficient  would  not  be  an  adequate  index  of  the 
real  connection  between  the  phenomena.  The  de- 
tails of  the  computation  of  the  above  coefficients 
have  made  it  abundantly  clear  that  the  interrela- 
tions between  the  size  of  the  establishment,  the  rate 
of  wag-es  and  the  aee  of  the  laborer  cannot  be.  suffi- 
ciently  described  by  the  simple  linear  laws  that  are 
obtained  in  the  usual  cases  of  correlation. 

Let  us  first  endeavor  to  find  the  law  of  the  varia- 
tion of  wages  with  the  age  of  the  laborer. 

Tables  I  and  II  of  the  text  have  been  computed 
from  Table  IV  of  the  Appendix.1  Knowing  the 
mean  ages  of  the  laborers  in  the  separate  wage  groups 
and  the  mean  wages  earned  by  laborers  in  the  same 

1  Table  IV  of  the  Appendix  was  copied  from  the  publication,  La 
Donna  Nell'  Indtistria  fialiana.  pp.  OU-100. 


142 


Laws  of  Wages 


TABLE   I.  —  Mean  Daily  Wages  of   Italian  Women   accord- 
ing to  TiiKii:  Aces  and  the  Sizes  of  the  Establishments  in 

WHICH    THEY    WERE    AT    WORK 


Age  or 
Employees 

Mean  Daily  Wages  received  in  Establishments  with 

Less  than  20 
Employees 

20-99 

100-499 

500  and  Over 

15-20 

.87 

.93 

1.04 

1.24 

20-35 

1.09 

1.10 

1.21 

1.50 

35-55 

1.05 

1.12 

1.17 

1.48 

Above  55 

.92 

.98 

.98 

1.16 

TABLE  II.  —  Mean  Ages  of  the  Employees  in  the  Several 
Age  Groups  of  the  Four  Classes  of  Establishments. 
Textiles.     Italy. 


Size  of 
Establishment 

Age  Groups 

Above  15 

15-20 

20-35 

35-55 

Above  55 

Less  than  20 
employees 

28.23 

17.32 

25.82 

44.43 

58.20 

20-99 

25.03 

17.30 

25.33 

44.72 

57.53 

100-499 

25.14 

17.30 

25.22 

44.89 

57.58 

500  and  Over 

24.32 

17.31 

25.34 

43.63 

57.49 

groups,  we  can  deduce  the  approximate  law  of  the 
variation  of  wages  with  the  age  of  the  laborer.  Fig- 
ure 18  is  the  graphical  description  of  the  variation  of 
wages  with  the  age    of   the   female  workers,  above 


Wages  and  (he  Concentration  of  Industry      1  13 

fifteen  years  of  age,  engaged  in  the  manufacture  of 
textiles  in  Italy.  The  four  curves  upon  the  chart 
give  the  variation  of  wages  with  the  age  of  the  la- 
borer, for  the  establishments  of  different  sizes. 

The  curves  show  :  — 

(1)  That  the  law  of  the  variation  of  wages  with 

the  age  of  the  laborer  is,  in  general  charac- 
ter, the  same  in  establishments  of  different 
sizes :  There  is  a  rapid  rise  of  wages  to  a 
maximum,  between  twenty-five  and  thirty- 
five  years  of  age,  and  a  slow  descent  to  old 
age. 

(2)  That  the  larger  the  establishment  the  higher 

the  wages  at  all  ages.  (This  may  be  partly 
due  to  the  fact  that  data  from  the  whole  of 
Italy  were  mixed  in  the  summary  table  that 
has  been  used.) 

(3)  That  in  case  of  the  smaller  establishments  — 

establishments  "less  than  20  employees," 
and  between  "20  and  99  employees" — the 
wages  of  the  old  employees  are  higher  than 
the  wages  of  the  young  employees,  while 
the  contrary  is  true  of  the  larger  establish- 
ments. (Compare  the  columns  in  Table  I 
of  the  text.) 

(4)  That  the  descent  from  the  maximum  wage  is 

more  rapid  in  the  large  establishments.1 
(Compare  the  curves  in  Figure  18.) 

1  The  above  method  and  conclusions  are  submitted  as  contribu- 
tions to  Professor  Max  Weber's  problem  :     "  Es  1st  eine  der  mchtig- 


144 


Laws  of  Traces 


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Wage*  and  the  Concentration  of  Industry       I  \~> 

"Why  should  the  law  of  the  variation  of  wages 
with  aire  take  this  peculiar  form?  Why  should  there 
be  a  rapid  rise  to  a  maximum  between  twenty-five 
and  thirty-live  years  of  aire  and  a  slow  descent  to  old 
age?  And  why  should  the  graphs  descriptive  of  the 
operation  of  the  law  in  the  four  classes  of  estab- 
lishments be  disposed  in  the  same  order  as  the  sizes 
of  the  establishments  ?  The  productivity  hypothesis 
supplies  the  proper  answer  to  all  of  these  questions. 

We  shall  consider  first  the  bearing  of  the  produc- 
tivity hypothesis  upon  the  shape  of  the  age-wage 
curve.  In  Chapter  IV  we  found  that  the  efficiency 
of  the  laborer  is  dependent  upon  a  balance  of  physi- 
cal, mental,  and  moral  qualities,  and  that  the  wage  of 
the  laborer  is  dependent  upon  his  industrial  efficiency. 
In  the  present  chapter  wre  have  discovered  the  law  of 
the  variation  of  wages  with  the  age  of  the  laborer. 
If  the  productivity  hypothesis  be  the  true  explanation 
of  wages,  it  would  follow  that  the  efficiency  of  the 
laborer  —  his  balance  of  physical,  mental,  and  moral 
qualities  —  must  vary  with  age  in  a  manner  similar 


sten  Aufgaben,  fur  die  einzelnen  Industrien,  innerhalb  ihrer  die  ein- 
zelnen Avbeiterkategorien  und  fur  diese  \viedi>r  nach  den  einzelnen 
ethnischen,  sozialen  und  Berufs-Provenienzen  festzustellen :  wie 
schnell  oder  lan^sam  sie  ein  solches  Mass  von  Leistungsflihigkeil 
erlangen,  dass  dire  Verwendung  als  Vollarbeiter  rentabel  wird,  wann 
sie  den  Hohepunkt  ilirer  Leistung  erreichen,  wie  lange  sie  sich  auf 
dieser  Hohe  behaupten,  und  wann  ihre  Leistungsfahigkeit  so  weit 
sinkt,  dass  .sie  nicht  mehr  als  Vollarbeiter, oder  schliesslich  iiberhaupi 
nicht  mehr  fiir  die  betrcnVnde  Arbeitsart  verwendbar  sind."  "  Zur 
Psychophysik  der  industriellen  Arbeit,"  Archiv  fur  Sozialwissens 
und  Sozialpolitik,  1909,  pp.  270-271. 


146  Laws  of  Wages 

to  the  variation  of  wages  with  age:  it  must  rise 
rapidly  to  a  maximum  between  twenty-five  and 
thirty-five  years  of  age  and  then  descend  slowly  to 
old  age.  There  can  be  very  little  doubt,  I  think,  that 
amono-  the  mass  of  laborers  industrial  efficiency  varies 
with  age  according  to  this  law.  The  study  of  certain 
physical  measurements  is  confirmatory  of  this  belief. 
In  a  paper  by  A.  O.  Powys  on  "  Data  for  the  Prob- 
lem of  the  Evolution  in  Man,"  1  the  following  im- 
portant truths  are  discovered  :  — 

(1)  The  law  of  the  variation  of  stature  with  age, 

in  case  of  the  experience  of  New  South 
Wales,  is  that  stature  increases  rapidly  from 
the  age  of  fifteen  to  a  maximum  between 
twenty-five  and  thirty  years  of  age  and  then 
decreases  slowly  to  old  age.  (The  maxi- 
mum stature  of  men  is  reached  at  about 
twenty-eight  years  of  age  and  of  women  at 
about  twenty-five.) 

(2)  "  The  modal  fertility  of  Victorian  women  is  at 

27  and  of  Victorian  men  at  32.  For  New 
South  Wales  women  the  modal  fertility  24.4, 
two  to  three  years  less  than  for  Victoria. 
We  have  not  the  data  for  New  South  Wales 
men,  but  they  would  probably  show  a  mode 
of  about  29-30  instead  of  32.  Thus  we  see 
that  the  age  of  maximum  fertility  at  any 
rate  approaches,  if  it  does  not  coincide  with, 
the  age  of  most  fully  developed  stature.     As 

1  Biometrika,  Vol.  I,  pp.  30-49. 


Wages  and  the  Concentration  of  Industry      1  1" 

Mr.  Powys  remarks,  this  tendency  of  maxi- 
mum stature  age  to  coincide  with  that  of 
maximum  fertility  can  hardly  he  fortuitous. 
It  seems  probahle  that  in  man,  as  in  other 
types  of  life,  the  age  of  maximum  fertility 
is  the  age  of  most  fully  developed  physique."  1 

The  law  of  the  variation  of  wages  with  age  is 
therefore  similar  to  the  law  of  the  development  of 
physique,  and  both  fertility  and  industrial  efficiency 
reach  their  maxima,  in  the  mass  of  laborers,  at  about 
the  period  of  most  fully  developed  physique.  This 
resemblance  in  the  general  character  of  the  law  of 
the  development  of  physique  and  the  law  of  the  vari- 
ation of  wages  with  age,  together  with  the  approxi- 
mate coincidence  of  the  periods  of  fully  developed 
physique,  maximum  fertility,  and  maximum  industrial 
efficiency  leaves  very  little  room  for  doubt  as  to  the 
intimate  causal  relation  of  the  phenomena.  The  facts 
are  all  in  harmony  with  the  a  priori  doctrine  that 
the  laborer's  income  is  dependent  upon  his  efficiency, 
and  that  consequently  the  law  of  the  variation  of  his 
income  is  similar  to  the  law  of  the  variation  of  his 
efficiency. 

We  may  now  consider  the  manner  in  which  the 
productivity  hypothesis  supplies  the  answer  to  the 
question  as  to  why  the  graphs  descriptive  of  the  varia- 
tion of  wages  with  the  age  of  the  laborer  are  disposed 

1  Remarks  of  Professor  Pearson  upon  Mr.  Powys'  data,  Biometrika, 
Vol.  I,  p.  48. 


1  is  Laws  of  Wages 

upon  the  chart  in  the  same  order  as  the  sizes  of  the 
establishments. 

Two  points  may  be  made :  — 

(1)  The  large  establishments  select  the  more  effi- 
cient laborers.  Referring  to  the  payment  of 
higher  wages  in  large  establishments,  the 
French  report  Salaires  et  duree  du  travail 
dans  V Industrie  frangaise  makes  the  following 
observation :  — 

"  Cette  tendance  ne  se  manif este  pas  seulement  en  f aveur 
cles  industries  qui,  comme  les  mines,  les  usines 
metallurgiques,  les  compagnies  de  transport,  sont  le 
terrain  propre  de  la  grande  industrie  :  on  Vobserve 
encore  dans  d'autres  groupes  ok  les  grands  etablisse- 
ments  compensent,  par  des  avantages  economiques 
certains,  la  contrainte  morale  que  la  concentration  des 
e nf  reprises  impose  a  la  population  ouvriere,  laquellene 
renonce  pas  sans  regret  a  la  vie  plus  irreguliere,  mais 
en  un  sens  plus  independante,  de  Vancienne  Industrie 


» i 


(2)  Because  of  the  use  of  large  fixed  capital  in 
large  establishments,  the  more  efficient 
workers  are  more  valuable  to  the  large  than 
to  the  small  establishments. 

'•  We  have  hitherto  supposed  that  it  is  a  matter  of  in- 
difference to  the  employer  whether  he  employs  few 
or  many  people  to  do  a  piece  of  work,  provided  his 
total  wages-bill  for  the  work  is  the  same.  But  that 
is  not  the  case.     Those  workers  who  earn  most  in  a 

1  Vol.  IV,  p.  22.     I  have  italicized  the  part  of  the  quotation  that  I 
wish  to  emphasize. 


Wages  and  the  Concentration  of  Industry       L49 

week  when  paid  at  a  given  rate  for  their  work  are 

those  who  are  cheapest  to  their  employers  (ami 
ultimately  to  the  community,  unless  indeed  they 
oversl  rain  t  liemselves,  and  work  1  nernselves  out  pre- 
maturely). For  they  use  only  the  same  amount  of 
fixed  capital  as  their  slower  fellow  workers;  and, 
since  they  turn  out  more  work,  each  part  of  it  has  1" 
bear  a  less  charge  on  this  account.  The  prime  costs 
are  equal  in  the  two  cases ;  but  the  total  cost  of  thai 
done  by  those  who  are  more  efficient,  and  get  the 
higher  time- wages,  is  lower  than  the  total  cost  of 
that  done  by  those  who  get  the  lower  time-wages  at 
the  same  rate  of  piece-work  payment."  "This  point 
is  seldom  of  much  importance  in  out-of-door  work, 
where  there  is  abundance  of  room,  and  comparatively 
little  use  of  expensive  machinery  ;  for  then,  except 
in  the  matter  of  superintendence,  it  makes  vei\ 
little  difference  to  the  employer,  whose  wages-bill 
for  a  certaiu  piece  of  work  is  £100,  whether  thai 
sum  is  divided  between  twenty  efficient  or  thirty 
inefficient  workers.  But  when  expensive  machinery 
is  used  which  has  to  be  proportioned  to  the  number  of 
workers,  the  employer  would  often  find  the  total  cost  oj 
his  goods  lowered  if  he  could  get  twenty  men  to  turn 
out  for  a  wages-bill  of  £50  as  much  work  as  he 
hail  previously  got  done  by  thirty  men  for  a  vages-hdl 
of£40."x 

We  infer  from  the  quoted  facts  that  the  higher 
wages  paid  in  the  larger  establishments  are  duo  to 
the  greater  productivity  of  a  personnel  which,  age  for 
age,  is  superior  in  a  balance  of  physical,  mental,  and 
moral  qualities. 

1  Marshall:  Principles  of  Economics,  4th  edit.,  pp.  631-632.  The 
part  of  the  quotation  that  I  wish  to  stress  I  have  italicized. 


150  Laws  of  Wages 

The  next  detail  to  be  examined  is  that  of  the  dif- 
ferences in  the  age  grouping  of  the  operatives  in  large 
and  in  small  establishments.  The  curves  descriptive 
of  the  frequency  distributions  according  to  the  age  of 
the  employees  in  establishments  of  different  sizes  may 
be  deduced  from  Table  IV  of  the  Appendix.  The 
method  that  I  have  adopted  may  be  understood  from 
the  following  illustration.  Table  IV  gives  the  infor- 
mation that,  in  establishments  employing  at  least  500 
women,  41.9  per  cent  of  the  employees  were  between 
15  and  20  years  of  age  ;  47.3  per  cent  between  20  and 
35 ;  9.8  per  cent  between  35  and  55;  and  1  per  cent 
over  55.  Assuming  that  no  employee  was  over  65  years 
of  age,  the  preceding  age  distribution  may  be  expressed 
in  cumulative  form  as  follows:  100  per  cent  were 
over  15  years  of  age ;  58.1  per  cent  over  20  years  of 
age  ;  10.8  per  cent  over  35 ;  1  per  cent  over  55 ;  and 
zero  over  65.  By  fitting  a  parabola  of  the  fourth 
order  to  the  age  distribution  in  the  cumulative  form, 
the  equation  to  the  age  distribution  is   found  to  be 

y  =  7.167674  -  .518268  x  +  .028171  x*  -  .0023708  a? 
+  .000064577  x\ 

where,  the  origin  being  taken  at  40,  (40  +  .t,)  repre- 
sents the  age  and  y  the  cumulative  percentage 
frequency.  By  differentiating  the  equation  and 
changing  the  signs  of  the  quantities,  the  frequency 
distribution  according  to  age  is  obtained  in  the  usual 
form.  The  equation  in  the  differential  form  is 
y  =  .518268  -  .056342  x  +  .00711 24  x2  -  .0002583  x\ 


Wages  and  the  Concentration  of  Industry       1">1 


From  this  latter  equation,  since  the  origin  is  at  40, 
the  mean  of  the   distribution    may  be    found    from 

/  yxdx 


40  +  —  and    the    standard    deviation    of    the 


distribution    from 


i/r'dx         I    yxdx 


Inas- 


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i>  L  Jb  J 

much  as  the  lower  age  limit  in  the  four  groups 
of  establishments  is  15  years  of  age,  b,  the  lower 
limit  of  integration,  is  —  25.  The  upper  limit  of  inte- 
gration, a,  is  determined  by  the  point  where  the 
curve  cuts  the  axis  of  x  and  is  different  in  the  four 
types  of  establishments. 

By  utilizing  this  method,  Table  III  of  the  text  is 
derived. 


TABLE  III.  — Means  and  Standard  Deviations  of  the  Ages 
of  Employees,  according  to  the  Sizes  op  the  Establish- 
ments 


Si/k.  of  Establish ments 

Below  20 

Employees 

20-99 

100-499 

500  and 

Over 

Mean  Age 

28.23 

25.63 

25.14 

24.32 

Standard  Deviation  .     .     . 

12.lT) 

10.84 

10.59 

9.37 

We  see  from  this  table  that — 
(1)  the  larger  the  establishment,  the  lower  is  the 
mean  age  of  the  employees ; 


152 


Laws  of  Wages 


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Wages  and  the  Concentration  of  Industry      L53 

(2)  the  larger  the  establishment,  the  smaller  is  the 
"  scatter  "  about  the  mean  age. 

It  follows  from  these  two  facts  that  the  bulk  of 
the  adult  personnel  in  the  four  classes  of  establish- 
ments is  younger,  the  larger  the  establishments. 

In  Figure  19  the  percentage  distribution  of  the 
operatives  in  the  four  classes  of  establishments  is 
roughly  indicated  by  a  series  of  broken  lines.  The 
most  marked  feature  of  the  graphs  is  that  above 
forty  years  of  age  the  percentage  frequencies  are  in 
inverse  order  of  the  sizes  of  the  establishments  —  the 
smaller  establishments  having  at  all  ages  above  40  a 
larger  percentage  of  workwomen  than  the  large 
establishments. 

Amount  of  Emjiloyment. 

We  come  now  to  the  consideration  of  the  relation 
of  the  size  of  the  establishment  in  which  laborers  are 
at  work  to  the  amount  of  employment  afforded 
by  the  establishments  in  the  course  of  the  year. 
We  shall  seek  to  know  whether  the  mean  num- 
ber of  days  in  which  the  laborers  are  employed 
in  a  year  bears  any  relation  to  the  size  of  the  estab- 
lishment in  which  they  are  at  work.  The  material 
used  in  the  investigation  is  again  drawn  from  the 
admirable  report,  La  Donna  NelV  Iinlitstria  Italiana. 

In  the  Appendix,  Table  V,  which  was  compiled 
from  the  Italian  report,  summarizes  the  data  relating 
to  the  manufacture  of  textiles.  From  this  Table  V 
two  contingency  tables  —  Tables    IV  and  V  of   the 


154 


Lairs  of  Wages 


TABLE  IV. —  Contingency  between  the  Amount  of  Employ- 
ment and  the  Size  of  Establishments.  Textiles.  La 
Donna  Nell'  Industkia  Italiana. 


Mean  Number 

of  Days,  per 

Establishment, 

worked  in 

a  Year 

Number  of  Women  in  Establishments 
of  Sizes  given  Below 

Total 

Less 
than  20 

20-99 

H  (0-499 

500  and 
Over 

245-255 

1167 

25,007 

26,174 

255-265 

62,930 

62,930 

265-275 

999 

6789 

7788 

275-285 

3772 

3772 

285-295 

3744 

25,700 

29,444 

295-305 

4936 

16,269 

21,205 

Total 

2166 

32,523 

93,566 

23,058 

151,313 

text  —  have  been  constructed.  Both  of  the  contin- 
gency tables  refer  to  the  relation  of  the  amount  of 
employment  to  the  size  of  the  establishment,  but 
they  differ  in  respect  to  the  system  of  weighting  the 
amount  of  employment.  The  original  Italian  report  * 
gives  the  number  of  establishments  of  various  sizes, 
the  mean  number  of  days,  per  establishment,  worked 
during  the  year  by  the  establishments  of  the  several 
sizes,  and  the  total  number  of  workwomen  over  fifteen 

1  Pages  54-62. 


Wages  and  the  Concentration  of  Industry       L55 

TABLE  V.  —  Contingency  between  the  Amount  <>i  Employ- 
ment and  the  Size  of  Establishments.  Textiles.  La 
Donna  Nell'  [ndustria   Iiaiiaxa. 


M  i:  in    Ni  Mm  B 
hi     Days,    pek 

Establishment, 

WOBKBD    is     \ 

Tear 

N  i  \iu kk  ok  Establishments  of  Sizes  gives  Below 

Total 

Loss  than  20 
Employees 

20-99 

100-199 

500  and 

(  Kit 

245-255 

116 

613 

729 

255-265 

162 

462 

2G5-275 

12:} 

11 

134 

275-285 

92 

92 

2S5-295 

99 

130 

229 

295-305 

• 

27 

26 

53 

Total 

239 

804 

619 

37 

1699 

years  of  age  employed  in  the  establishments  of  the 
several  classes,  on  the  30th  of  November,  1903. 

In  the  contingency  Table  IV,  the  mean  number  of 
days  worked  in  a  year,  per  establishment,  is  weighted 
in  each  case,  with  the  number  of  workwomen  em- 
ployed in  the  establishments  of  the  class  in  question, 
on  the  30th  of  November,  1003.  For  example,  1 1 1  > 7 
women  over  15  years  of  age  were  employed,  on  the 
30th  of  November,  1903,  in  establishments  in  which 
the  mean  number  of  days'  work,  per  establishment,  in 
the  preceding  year,  was  between  245  and  255. 


156  Laws  of  Wages 

In  the  contingency  Table  V,  the  mean  number  of 
days  worked  in  a  year,  per  establishment,  is  weighted 
in  each  case  with  the  number  of  establishments  of 
the  various  sizes  falling  within  the  limits  of  the  par- 
ticular "days  worked"  group.  For  example,  116 
establishments  employing  less  than  20  women  each 
worked  on  the  average  between  245-255  days,  in  the 
year  from  December  1,  1902,  to  November  30,  1903. 

When  the  coefficients  of  contingency  are  calculated 
in  the  usual  way  from  these  two  tables,  we  find  that  — 

(1)  in  the  first  system  of  weighting,  Table  IV, 

(71  =  .791;    <X=.89; 

(2)  in  the  second  system  of  weighting,  Table  V, 

Ci=.785j  C,  =  .88. 

These  very  high  coefficients  are  marked  indications 
of  the  gains  to  laborers,  in  the  way  of  amount  of  em- 
ployment, that  accrue  in  consequence  of  the  superior 
management  necessitated  by  the  investment  of  vast 
capital  in  enterprises  producing  upon  a  large  scale. 

Continuity  of  Employment. 

The  third  aspect  of  our  problem  as  to  the  relation 
of  the  status  of  the  laborer  to  the  size  of  the  estab- 
lishment in  which  he  is  employed  is  concerned  with 
the  variability  of  the  amount  of  employment  in  course 
of  the  year.  It  has  just  been  proved  that  the  larger 
the  establishment,  the  greater  the  amount  of  annual 
employment.     We   now   inquire   as    to   whether  the 


Wages  and  the  Concentration  of  Industry      157 

amount  of  employment  afforded  by  the  establish- 
ments of  the  various  sizes  is  more  or  less  variable, 
from  month  to  month,  in  the  larger  establishments 
than  in  those  of  the  smaller  types. 

Table  VI  of  the  text,  referring  to  the  manufacture 
of  textiles  in  Italy,  was  summarized  from  the  report 
that  has  proved  so  valuable  in  the  other  investiga- 
tions of  this  chapter.  It  gives,  for  establishments  of 
various  sizes,  the  monthly  indices  of  employment,  in 
the  more  important  subdivisions  of  the  textile  indus- 
try, together  with  the  minimum,  mean,  and  maxi- 
mum monthly  variations,  in  the  year  December  1, 
1902,  to  November  30,  1903. 

The  method  of  presenting  these  results  is  due  to 
Professor  Bagni,1  who  had  charge  of  the  preparation 
of  the  report,  La  Donna  NelV  Industria  Italiana. 
Before  commenting  upon  the  data  of  Table  VI,  we 
shall  consider  the  method  of  computing  the  monthly 
indices  of  employment. 

For  every  establishment  investigated,  the  Italian 
Bureau  of  Labor  had  data  showing,  for  each  month 
in  the  year  December  1,  1902,  to  November  30, 1903, 
the  number  of  days  in  which  the  establishment  was 
in  operation  and  the  mean  daily  number  of  work- 
women who  were  employed.  It  was,  therefore,  pos- 
sible to  compute  for  each  class  of  establishments 
the  total  number  of  workwomen-days-work  in  each 
month.  For,  obviously,  the  number  of  workwomen- 
days-work  in  establishment  A'  during  the  month  T 

1  La  Donna  Nell'  Industria  Italiana,  p.  ix. 


158 


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160  Laws  of  Wages 

was  equal  to  the  number  of  clays  the  establishment 
was  in  operation  multiplied  by  the  average  daily 
number  of  workwomen  employed  that  month.  By 
means  of  this  method  the  number  of  workwomen- 
days-work  in  each  of  the  four  groups  of  establish- 
ments was  computed  for  each  month  of  the  year 
and  for  the  whole  year.  The  monthly  numbers  were 
afterwards  expressed  as  fractions  of  the  correspond- 
ing- annual  numbers,  and  the  fractions  were  then 
multiplied  by  1200.  The  resulting  numbers  are  Pro- 
fessor Bagni's  monthly  indices  of  employment.  The 
maximum,  mean,  and  minimum  variations  are  meas- 
ured from  100. * 

We  may  now  examine  Table  VI.  By  referring  to 
the  last  two  columns  we  observe  that  — 

(1)  As  the  size  of  the  establishment  increases,  the 

general  trend  of  the  mean  variations  of  the 
index  of  employment  is  downward.  (The 
silk  industry  is  an  exception  to  the  rule.) 

(2)  As  the  size  of  the  establishment  increases,  the 

general  trend  of  the  maximum  deviation  is 
downward.  (The  silk  industry  is  again  an 
exception  to  the  rule.) 

(3)  In  all  of  the  groups,  the  mean  deviation  and 

maximum  deviation  in  the  largest  establish- 
ments are  smaller  than  the  corresponding 
deviations  in  the  smallest  establishments. 

1  The  objection  to' this  method  is  that  spurious  monthly  differences 
are  introduced  in  consequence  of  not  taking  into  account  the  differ- 
ences in  the  length  of  the  calendar  months.  The  defect  in  the 
method  does  not  invalidate  the  inferences  in  the  text. 


Wages  and  the  Concentration  of  Industry       L61 

Length  of  the   Working  Day. 

The  fourth  aspect  of  the  problem  as  to  the  relation 
of  the  status  of  the  laborer  to  the  size  of  the  estab- 
lishment in  which  he  is  employed  is  concerned  with 
the  length  of  the  working  day.  Up  to  this  point  the 
researches  of  this  chapter  have  been  based  upon  the 
data  relating  to  the  textile  industry  in  Italy.  It 
would  be  highly  desirable  to  have  all  of  our  conclu- 
sions bearing  upon  the  concentration  of  industry  re- 
late to  one  industry  at  a  given  time  and  place.     But 

TABLE  VIL  — Mean  Duration  of  Daily  Hours  of  Work, 
considered  in  relation  to  the  slze  of  estarlishm  kn'ts, 
in  the  Mines  of  France  producing  Coal  and  Other 
Fuel 


Locality 

Mean  Durati"n   of   Daily    Hours  >>y   Work 

ACCOkdin<;    as    the    Establishment    hah   a 
Ni  mi;ek  OF  Workmen 

Exceeding 
999 

From  500 
to  999 

From  100 
t.)  499 

From  '-'."> 
to  99 

From  1 

to  -.'4 

Region  Nord  et  Pas-de- 

8| 

n 

9} 

Region  Est 

81 

9 

10J 

lir-gion  Centre    .... 

9 

91 

9J 

10 

Region  Sud 

93 

H 

10 

Region  Sud-Est  .... 

*i 

10 

9* 

1  kggion  Bouches-du-Rhone 

8} 

8J 

M 


162  Lairs  of  Wages 

I  do  not  know  of  the  existence  of  material  presenting 
a  classification,  according  to  sizes  of  establishments, 
of  the  hours  of  labor  in  the  manufacture  of  textiles 
in  Italy. 

In  default  of  appropriate  Italian  figures,  we  may 
refer  to  the  investigation  embodied  in  the  French 
report:  Salaires  et  duree  du  travail  dans  V Industrie 
frangaise.  Table  VII ]  is  given  as  a  favorable  in- 
stance of  the  findings  of  the  French  statisticians. 
This  table  eliminates  the  differences  in  hours  of 
labor  arising  from  the  differences  in  locality,  and  it 
clearly  shows  that  as  a  general  rule  the  hours  of  labor 
decrease  as  the  size  of  the  establishment  increases. 

The  conclusion  that  is  drawn  from  this  illustration 
is  the  conclusion  of  the  French  report  as  to  the 
general  trend  in  the  whole  of  the  French  provincial 
manufactures.  The  conditions  of  production  in  Paris 
are  exceptional,  and  statistical  study  of  the  relation 
of  the  size  of  the  establishment  to  hours  of  labor  is 
rendered  difficult  because  of  the  classification  under 
the  same  name  of  industries  that  are  radically  differ- 
ent in  character.  "  En  province,  au  contraire,  les 
fabrications  sont  plus  courantes,  les  divers  etablisse- 
ments  groupes  sous  le  meme  nom  d'industrie  forment 
des  groupes  plus  homogenes.  On  peut  meme  les 
etudier,  et  on  observe  nettement  une  amelioration  des 
conditions  du  travail  dans  les  grandes  entreprises. 
Dans  leur  ensemble,  la  duree  du  travail  est  plus 
courte."  "- 

i  This  table  is  taken  from  Vol.  IV,  p.  100.  2  Ibid.,  p.  22. 


Wages  and  the  Concentration  of  Industry       L63 

We  started  out  to  find  the  relation  of  the  concen- 
tration of  industry  to  the  changing  status  of  the 
laborer,  and  we  proposed  to  investigate  that  relation 
I  mm  the  four  points  of  view  of  (1)  the  rate  of  wages, 
(2)  the  amount  of  employment,  (3)  the  continuity  of 
employment,  and  (4)  the  length  of  the  working 
day.  Our  investigation  has  yielded  the  definite 
result  that,  as  the  size  of  the  establishment  increases, 
the  condition  of  the  laborer  improves  in  all  directions 
—  his  wages  rise,  he  is  employed  a  greater  number  of 
days  in  a  year,  his  employment  varies  less  from 
month  to  month,  and  his  hours  of  labor,  per  day, 
decrease. 

We  have  found  that  the  law  of  the  variation  of 
wages  with  the  ao;e  of  the  laborer  is  similar  in  estab- 
lishments  of  all  sizes,  and  that  the  general  character 
of  the  law  has  its  explanation  in  the  law  of  the  de- 
veloping physique  and  capacity  of  the  laborer.  The 
differences  in  the  graphs  representative  of  the  law  of 
the  variation  of  wages  with  the  age  of  the  laborer  in 
the  four  types  of  establishments  are  clue  to  the  large 
establishments  selecting  the  more  capable  workers. 
The  large  establishments  are  able  to  carry  out  the 
work  of  selection  because,  in  consequence  of  their 
large  capital  and  better  organization,  they  offer  op- 
portunities for  the  more  capable  laborers  to  reap  the 
reward  of  their  differential  ability. 


164 


Laws  of  Wages 


APPENDIX 


TABLE  I.  —  Contingency  between  the  Daily  Rate  of  Wages 
and  the  Size  of  the  Establishment  in  which  Employees 
were  at  Work.     Textiles.     Italy. 


Bate  of 
Wages  in 

Like  and 
Centesimi 

Number  of  Wobkwomen  in  Establishments  with 

Totals 

Less  than  20 
Employees 

From 
20-99 

From 
100-499 

500 
and  Over 

Up  to  .50 

150 

545 

1030 

96 

1821 

.51-. 75 

443 

6303 

9356 

1103 

17,205 

.76-1.00 

873 

12,863 

30,523 

3718 

47,977 

1.01-1.50 

645 

11,239 

45,113 

10,605 

67,602 

1.51-2.00 

214 

1843 

7097 

6396 

15,550 

2.01-2.50 

30 

519 

1755 

1482 

3786 

Over  2.50 

6 

177 

613 

413 

1209 

Totals 

2361 

33,489 

95,487 

23,813 

155,150 

Wages  mid  the  Concentration  of  Industry     L65 


TABLE  IT.  —  Contingency  between  the  Daily  Rate  of  Wages 
and  the  Age  of  the  Laborer.     Textiles.     Italy. 


Ka  1 1:  OF   W  !iGK8 

IV 

Like  and  Centesimi 

\i'Mi;i:i:  OF   EMPLOYEES    WHOSE  Ai.K-  WEBB    IN  THE 
A'.F  3B01  Pfl 

Totals 

15-20 

20-35 

35-55 

■  55 

Up  to  .50 

1125 

228 

105 

63 

1821 

.51-.75 

11,000 

4063 

1478 

664 

17,205 

.70-1.00 

21,903 

18,843 

6049 

1182 

17,977 

1.01-1.50 

24,905 

33,884 

8010 

803 

07,602 

1.51-2.00 

41M 

9103 

2109 

154 

15.550 

2.01-2.50 

.  555 

2511 

676 

44 

3786 

Above  2.50 

9S 

807 

289 

15 

1209 

Totals 

64,070 

69,439 

18,716 

2925 

155.150 

166 


Laws  of  Wages 


TABLE  III.  —  Contingency  between  the  Age  of  Employees 
and  the  Size  of  the  Establishment  in  which  they  were 
at  Work.     Textiles.     Italy. 


Agk  in 
Years 

Number  of  Workwomen  in  Estaulishments  with 

Totals 

Less  than  20 
Employees 

20-99 

100-499 

500  and 
Over 

15-20 

778 

13,453 

39,851 

9988 

64,070 

20-35 

1005 

14,831 

42,367 

11,236 

69,439 

35-55 

471 

4543 

11,367 

2335 

18,716 

Over  55 

107 

662 

1902 

254 

2925 

Totals 

2361 

33,489 

95,487 

23,813 

155,150 

Wages  and  (he  Concentration   <>f  Industry      Hi, 

TABLE  IV.  —  Classification  of  Workwomen  accukdixi;  to 
their  Ages,  their  Hates  oe  Wages,  and  the  Sizes  <>i  the 
Establishments  in  which  they  were  employed.  Textiles. 
La  Donna  Nell'  Indi  stria  Italiana,  pp.  99-100 


SIZE  OP  THE 
ESTABLISH- 
MENTS 

Peboentaq]   op  Workwomen,  over  IS  Sears  op  Age, 
receiving    the    following     rate     of      wages. 
[Rates  are  expressed  in  Centebimj  am>  Libi  | 

Age  Groups 

Up  to 
.50 

.51- 

.75 

.70- 
1.00 

1.01- 

1.50 

1.51- 

2.00 

2.01- 
2.50 

Above 

2.50 

Tutal 
Per- 
centage 

Less  than 

l'ii 
Employees 

4.0 

8.5 

12.1 

7.0 

1.3 

32.9 

15-20 

1.3 

<;.i 

15.0 

13.3 

5.4 

1.0 

.2 

16.6 

20-35 

.5 

3.0 

8.2 

6.0 

2.1 

.3 

20.1 

35-55 

.5 

.9 

1.7 

1.0 

.3 

4.4 

Above  55 

6.3 

18.8 

37.0 

27.3 

9.1 

1.3 

.2 

100.0 

20-99 

1.2 

11.1 

15.6 

11.2 

.9 

.2 

40.2 

15-20 

.2 

5.9 

it;.:, 

17.1 

3.3 

1.0 

.3 

44.3 

20-35 

.1 

1.6 

5.4 

4.8 

1.2 

.3 

.2 

13.6 

35-55 

.1 

.3 

.9 

.5 

.1 

1.9 

Above  55 

1.6 

18.9 

38.4 

33.6 

5.5 

1.5 

.5 

100.0 

100-llii) 

.9 

6.5 

ll.li 

17.1 

2.0 

.2 

.1 

41.7 

15-20 

.1 

1.9 

12,1 

24.1 

4.3 

1.3 

.4 

44.5 

20-35 

.1 

.!) 

3.9 

5.5 

1.0 

.3 

.2 

11.9 

35-55 

.5 

.8 

.5 

.1 

1.9 

A.bove  55 

1.1 

!I.S 

32.0 

47.2 

7.4 

1.8 

.7 

100.0 

500  and 
Over 

.3 

3.7 

!l.l 

19.5 

8.1 

1.1 

.1 

11 II 

15-20 

.1 

.6 

4.9 

20.5 

15.8 

4.1 

1.0 

1.3 

47.3 

20-35 

o 

1.3 

4.1 

2.9 

.3 

9.8 

:;:.  55 

.1 

.3 

.5 

.1 

1.0 

Above  55 

.4 

4.6 

1 .-).(! 

44.6 

2i;.<) 

6.2 

1.7 

100.0 

16S 


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CHAPTER    VII 

CONCLUSIONS 

"  Womit  wir  es  hier  zu  than  haben,  ist  eine  kommunistische 
Gesellschaft,  nicht  wie  sie  sich  auf  ihrer  eigenen  Grundlage  entwick- 
elt  hat,  sondern  umgekehrt,  wie  sie  eben  aus  der  kapitalistischen 
Gesellschaft  hervorgeht;  die  also  in  jeder  Beziehung  okonomisch, 
sittlich,  geistig,  noch  behaftet  ist  niit  den  Muttermalen  der  alten 
Gesellschaft,  aus  deren  Schoos  sie  herkomint." 

—  Karl  Marx. 

In  the  preceding  chapters  we  have  been  concerned 
entirely  with  the  scientific  aspects  of  the  subjects 
that  came  before  us,  and  no  attempt  was  made  to 
indicate  the  practical  bearing  of  the  results  that  were 
established.  But  the  economist,  least  of  all  scientists, 
can  feel  content  with  the  simple  understanding  of 
the  laws  of  his  subject  matter.  He  desires  to  see 
what  guidance  they  may  afford  in  the  complicated 
life  of  his  own  time.  This  summary  will,  accord- 
ingly, be  concerned  primarily  with  the  relation  of  our 
results  to  actual  practice. 

We  may  notice  first  the  practical  character  of  Sta- 
tistical Economics.  It  was  pointed  out  in  the  first 
chapter  that  in  its  scientific  character,  Statistical 
Economics  proposes  this  twofold  object :  (1)  to  bring- 
to  the  test  of  representative  facts  the  hypothe- 
ses and  theorems  of  pure  economics;  (2)  to  supply 

L69 


170  Laics  of  Wages 

data,  in  the  form  of  general  facts  and  empirical  laws, 
for  the  elaboration  of  dynamic  economics.  Its  prac- 
tical service  is  performed  in  a  similar  way ;  for,  in 
giving  a  statistical  summary  and  interpretation  of 
the  material  relevant  to  the  economic  subject  under 
investigation,  it  supplies  the  means  by  which  general 
reasoning  may  be  brought  to  bear  upon  the  problems 
of  industrial  legislation.  A  short  account  of  the  way 
in  which  this  form  of  economic  science  has  come  into 
being  will  indicate  more  clearly  its  scope  and  bearing. 

Just  half  a  century  ago,  in  an  inspiriting  address 1 
on  "  The  Progress  of  Economic  Science  during  the 
Last  Thirty  Years,"  William  Newmarch  summarized 
what  he  regarded  as  the  greatest  achievement  of  the 
science  during  the  period  covered  in  his  survey. 

"  Looking  back  at  the  changes  and  the  experience 
of  which  this  is  a  rapid  outline,  it  appears  to  me  that 
I  shall  not  be  in  any  danger  of  misleading  the  Sec- 
tion if  I  suggest  that  probably  the  most  conspicuous 
and  important  fact  to  be  found  in  the  history  of  Eco- 
nomic Science  during  the  last  thirty  years  is  this  ; 
namely,  that  while  there  has  been  no  change  in  the 
objects  to  which  it  is  directed — no  change  in  the 
purposes  intended  to  be  worked  out  —  while  these 
objects  and  these  purposes  remain  the  same  in  their 
broad  and  general  aspect  as  they  have  been  from 

1  Newmarch  gave  the  address  as  President  of  Section  (F)  of  Eco- 
nomic Science  and  Statistics  of  the  British  Association  for  the  Ad- 
vancement of  Science.  The  address  is  published  in  the  Journal  of 
the  Statistical  Society,  1861,  pp.  451-407. 


Conclusions  171 

the  time  of  Adam  Smith,  there  has  been  a  marked 
change  in  the  Methods  according  to  which  Kconomic 
Science  is  cultivated.  It  has  ceased  to  be  an  abstract 
science, —  it  has  ceased  to  be  a  system  of  subtle  and 
ingenious  reasonings.  It  has  little  by  little,  and  by 
a  process  cautious  and  full  of  promise,  become  a 
science  almost  entirely  experimental.  We  have 
learned  that  in  all  questions  relating  to  human  so- 
ciety—  in  all  controversies  where  the  agency  of  hu- 
man beings  has  to  be  relied  upon  for  working  out 
even  the  smallest  results — we  have  learned  that  in 
these  inquiries  the  only  sound  basis  on  which  we 
can  found  doctrines,  and  still  more  the  only  safe  basis 
on  which  we  can  erect  laws,  is  not  hypothetical  de- 
duction, however  ingenious  and  subtle,  but  conclu- 
sions and  reasoning  supported  by  the  largest  and 
most  careful  investigation  of  facts.  This  vital  change 
of  method,  this  substitution  of  observation  and  ex- 
periment (and  for  our  present  purpose  the  two  words 
mean  very  much  the  same  thing)  for  deductions  ar- 
rived at  by  geometrical  reasoning,  seems  to  me  to  be 
the  most  prominent  fact  of  the  last  thirty  or  forty 
years,  as  regards  the  progress  of  the  branches  of 
knowledge  which  more  immediately  interest  us  in 
this  Section." 

The  negative  attitude  of  Newmarch  with  regard  to 
theoretical  economics  I,  of  course,  do  not  share.  The 
quotation  has  been  made  in  order  to  stress  his  point  of 
view  as  to  the  relation  of  economic  science  to  legisla- 
tion.    The  two  pervading  ideas  of  the  address  are. 


172  Laws  of  Wages 

first,  that  effective  legislation  must  be  based  upon  ex- 
perience, and,  secondly,  that  experience  must  be 
interpreted  by  the  statistical  method  :  "  we  claim  for 
Statistics  .  .  .  that  it  is  the  application  of  the  Exper- 
imental or  Baconian  method  to  the  several  divisions 
of  inquiry  which  relate  to  man  in  society.  We  say 
that  where  there  is  no  careful  application  of  the 
Statistical  method  —  in  other  words,  where  there  is 
an  absence  of  observation  and  experiment,  so  far  as 
observation  and  experiment  can  be  applied  to  men 
in  Societies  —  there  can  be  but  faint  hope  of  arriving 
at  the  truth  in  any  line  of  research  connected  with 
social  problems."  l 

In  the  works  of  Stanley  Jevons  is  found  the  devel- 
opment of  the  ideas  of  Newmarch  upon  this  subject. 
Jevons  observed  that  legislation  in  England  did  not 
proceed  without  what  is  commonly  called  statistical 
evidence,  but  the  statistics  were  not  always  of  the 
right  sort,  nor  were  the  statistical  inquiries  always 
conducted  according  to  "true  scientific  method."2 
Furthermore,  using  the  hint  in  Newmarch's  address, 
he  called  the  method  of  legislation  he  approved 
"  Baconian  legislation,"  and  he  thus  described  the 
principle  upon  which  it  should  proceed  :  "  What  I 
venture  to  maintain  is  that  Baconian  legislation  will 
always  proceed  by  reasoning  from  the  most  nearly 
proximate  and  analogous  experience  which  is  avail- 

1  Newmarch  :  Journal  of  the  Statistical  Society,  1861,  p.  457. 

2  Essay  on  "  Experimental  Legislation  and  the  Drink  Traffic." 
Mi'thoils  of  Social  Reform,  p.  250. 


Conclusions  L73 

able.      We  cannot  possibly  dispense  with  general  rea- 
soning, but  ive  should  use  it  as  sparingly  as  possible. 
We  should  choose,  as  it  were,  the  lowest  logical  elevation 
in  sight."  1 

The  part  of  the  quotation  that  I  have  italicized 
presents  the  point  of  view  I  should  like  to  urge. 
According  to  the  argument  of  the  chapter  on  "  Statis- 
tical Laws,"  the  statistical  economist  proceeds  by  a 
progressive  synthesis  from  individual  facts  to  general 
facts,  and  from  general  facts  to  statistical  laws.  He 
expresses  the  laws  in  their  mathematical  form,  and, 
where  it  is  possible,  he  measures  the  degrees  of  asso- 
ciation between  the  related  phenomena,  expressing 
them  as  coefficients  of  correlation,  correlation  ratios, 
or  coefficients  of  contingency,  as  the  case  may  be. 
Now  in  Baconian  legislation,  the  interpretation  by 
means  of  general  economic  reasoning  of  the  statistical 
laws  and  coefficients  of  association  constitutes  "  the 
lowest  logical  elevation  in  sight"  upon  which  legisla- 
tion can  be  effectively  based.  The  practical  work  of 
the  statistical  economist  bridges  the  gap  between 
general  reasoning  and  the  crude  facts.2 

lJevons:   The  State  in  Relation  to  Labor,  p.  24. 

2  This  conception  of  Statistical  Economics,  theoretical  and  applied, 
is  receiving  a  most  promising  development  in  tin'  contemporary  Italian 
school,  whose  organ  of  publication  is  the  Giomale  ii'',:  Economisti. 
Following  Professor  Pareto's  attempt  to  give  concreteness  to  the  theory 
of  distribution  by  basing  his  reasoning  upon  a  statist  Leal  law  summar- 
izing approximately  the  distribution  of  income  in  modern  societies, 
numerous  essays  appeared,  particularly  in  Italy,  in  which  Pareto's 
method  was  applied  in  the  treatment  of  other  social  phenomena.  Pro- 
fessor Pareto  himself,  asserting,  in  1907,  that  "the  progress  of  polit- 
ical economy  in  the  future  will  depend  in  great  part  upon  the  invest  i- 


174  Laws  of  Wqges 

Comma-  now  to  the  detailed  consideration  of  the 
practical  bearing  of  the  preceding  chapters,  we  may 
observe  with  reference  to  the  two  theories,  which  for 
the  sake  of  brevity  we  may  refer  to  as  the  subsistence 
theory  and  the  standard  of  life  theory,  that  their  per- 
sistence in  economic  literature  gives  color  to  the  be- 
lief that  wages  may  be  increased  in  other  ways  than 
through  an  increased  effective  productivity  of  the 
laboring  class.  This  is  particularly  true  in  regard  to 
the  doctrine  of  the  standard  of  life,  because  in  sup- 
port of  false  views,  Ricardo's  authority  may  be  cited : 
"  The  friends  of  humanity  cannot  but  wish  that  in  all 
countries  the  labouring  classes  should  have  a  taste  for 

gation  of  empirical  laws  that  are  derived  from  statistics"  (Giornale 
degli  Economist!,  Maggio,  1907,  p.  366),  has  spent  much  of  his  time  in 
perfecting  the  inductive,  statistical  tool  by  means  of  which  the  em- 
pirical laws  are  summarized  in  mathematical  form. 

But  the  formal  conception  of  an  Inductive  Economics,  utilizing  as 
means  of  investigation  modern  statistical  methods,  is  found  in  the 
w<  irk  of  Professor  Benini  and  of  Professor  Bresciani.  In  his  inaugural 
address  as  Professor  of  Statistics  in  the  University  of  Rome,  Professor 
Benini  outlined  his  conception  of  "  Una  possibile  creazione  del  metodo 
statistico.  L'economia  politica  induttiva"  {Ibid.,  Gennaio,  1908). 
His  volume  on  Principii  di  Statistica  Metodologica  may  be  regarded  as 
his  description  of  the  method  to  be  employed  in  the  treatment  of  this 
aspect  of  economic  science.  More  recently,  Professor  Bresciani,  in 
his  inaugural  address  as  Professor  of  Statistics  in  the  University  of 
Palermo,  has  treated  a  phase  of  the  same  subject  under  the  title 
"Sul  carattere  delle  leggi  statistiche  "  (Ibid.,  Marzo,  1910).  In  the 
series  of  articles  on  correlation  and  frequency  distributions,  published 
in  1909,  Bresciani  has  described  to  his  co-workers  the  methods  of  Pro- 
fessor Karl  Pearson.  A  marked  indication  of  the  influence  of  this 
constructive  group  of  younger  economists  is  seen  in  the  change  in 
t  he  name  of  their  journal.  Since  1910,  the  title  of  this  admirable 
review  is  no  longer  simply  Giornale  degli  Economisti  but  Giornale  degli 
Economist!  e  Statistica,  thus  establishing  a  formal  attempt  to  bring 
theoretical  and  statistical  economics  into  intimate  relation. 


Conclusions  L75 

comforts  and  enjoyments,  and  that  they  should  be 
stimulated  by  all  legal  means  in  their  exertions  to 
procure  them."  '  It  is  entirely  possible  with  ingenuity 
to  interpret  Ricardo's  meaning  from  the  context  so 
that  it  would  seem  to  be  in  harmony  with  the  modern 
doctrine,  but,  without  doubt,  the  vigorous  statement 
is  both  misleading  and  false:  misleading,  in  conse- 
quence of  wrong  emphasis  in  centering  attention 
upon  increasing  wants  while  ignoring  the  inevitable 
price  of  their  gratification;  and  false,  in  consequence 
of  lumping  together  the  "  laboring  classes,"  and  infer- 
ring that  it  is  true  of  all  grades  of  labor  that  there 
should  be  an  artificial  stimulation  of  wants. 

In  order  to  seize  the  degree  of  truth  in  either  of  the 
two  theories  that  we  are  considering,  it  is  necessary 
to  reason  about  laborers  not  as  a  class  that  may  be 
represented  as  a  whole  by  a  more  or  less  fictitious 
"  average  laborer,"  but  as  made  up  of  groups  which, 
in  regard  to  wages,  may  possibly  be  subject  to  differ- 
ent laws  or  to  different  degrees  of  effectiveness  in  the 
working  of  the  same  law. 

If,  with  this  conception,  we  begin  our  investigation 
by  considering  the  two  theories  with  reference  to  their 
relevancy  to  the  groups  of  skilled  and  of  unskilled 
laborers,  wre  are  brought  to  practical  conclusions  of 
considerable  importance  :  — 

(1)  It  cannot  be  said  thai  in  the  territory  covered 
by  our  figures  the  wages  of  unskilled  laborers 

1  Ricardo:  Principles  of  Political  Economyand  Taxation,  McCullochs' 

edit.,  p.  54. 


L76  •     Laws  of  Wages 

are  determined  by  the  cost  of  the  means  of 
subsistence,  that  is  to  say,  a  fixed  mode  of  life. 
This  negative  statement  is  a  fortiori  true  of 
the  wages  of  skilled  laborers ; 

(2)  There    is    a    close    correlation    between    the 

wages  of  unskilled  laborers  and  their  stand- 
ard  of  life,  but  the  correlation  is  not  so  high 
as  to  justify  the  inference  of  a  cause  and 
effect  relation  ; 

(3)  The  correlation  between  the  wages  of  skilled 

and  of  unskilled  laborers  is  much  higher  than 
the  correlation  of  the  wages  of  unskilled 
laborers  with  their  standard  of  life. 

These  facts,  which  are  inductively  established,  lead 
to  the  following  reflection :  the  wages  of  both  skilled 
and  of  unskilled  laborers  are  determined  by  other 
causes  than  the  adherence  of  the  laborers  to  a  fixed 
mode  of  subsistence  or  to  a  variable  standard  of  life. 
The  chief  determining  cause  is  the  specific  productive 
efficiency  of  each  group,  as  is  illustrated  in  Chapter 
III :  the  efficiency  of  the  unskilled  group  yields  a 
\\;i<ie  that  affords  a  variable  standard  of  life,  and 
because  of  the  great  supply  of  labor  of  this  character, 
both  the  wage  and  the  standard  of  life  vary  within 
narrow  limits.  The  wages  of  the  skilled  group  are 
likewise  dependent  upon  the  specific  productive  effi- 
ciency of  the  skilled  group,  but,  because  of  the  oppor- 
tunity enjoyed  by  employers  in  an  open  market  of 
substituting,  within  limits,  unskilled  for  skilled  labor, 


Conclusions  177 

the  strategic  advantage  of  skilled  laborers  is  affected 
by  the  wage  received  by  unskilled  laborers,  as  is  in- 
dicated in  Chapter  IV.  It  is  submitted  that  these 
facts  have  a  fundamental  bearing  upon  the  theory  of 
wages,  upon  the  conception  of  the  solidarity  of  in- 
dustry, and  upon  all  projects  having  in  view  the 
bettering  of  the  state  of  the  laboring  class  by  the 
establishment  of  a  legal  minimum  wage  with  the 
necessary  concomitant  regulation  of  the  supply  of 
unskilled  labor.1 

The  idea  of  the  solidarity  of  industry  receives  in-' 
creased    illumination    from    the    conclusions    of    the 
chapter  on  "  Wages  and  the  Productivity  of  Labor." 
It  was  there  established  — 

(1)  that  average  wages  increase  with  the  specific 

product  of  labor ; 

(2)  that  the  more  rapid  the  increase  of  capital  in 

the  industry,  the  more  rapidly  do  wages 
increase ; 

(3)  that    the    fluctuations    of    wages    about    their 

general  trend  are  inversely  correlated  with 
the  machine-power  with  which  the  laborers 
work.  It  is  true  that  these  points  were  es- 
tablished only  with  reference  to  the  one 
industry  for  which  we  could  obtain  adequate 
data,  but  there  is  the  great  satisfaction  of 
knowing  that  the  inductive  findings  with 
regard  to  this  one  industry  are  in  complete 

1  t'f.  The  Minority  Report  of  the  English  Poor  Law  Commission,  I'.^'K 

N 


178  Laws  of  Wages 

accord  with  the  conclusions  of  a  priori  reason- 


ing:. 


The  very  high  coefficients  of  correlation  measuring 
the  relation  between  the  variables  that  figure  in  these 
three  propositions  compel  the  acceptance  of  the  idea 
of  solidarity  which  sympathetic  supporters  of  the 
cause  of  the  laborers  too  frequently  ignore.  It  is 
clearly  indicated  that  one  of  the  most  valuable 
services  that  can  be  rendered  by  labor  organizations 
consists  in  using  their  power  to  induce  and  compel 
the  highest  possible  efficiency  of  plant  and  industrial 
organization.  The  resulting  increased  productivity 
will  supply  the  fund  from  which  increased  wages  may 
be  obtained,  and  a  permanently  increasing  wage  can 
be  secured  only  by  increasing  the  flow  of  the  specific 
products  of  labor. 

It  has  been  said  that  the  results  of  Chapter  III 
compel  the  acceptance  of  the  idea  of  solidarity  of 
industry.  It  is  not  useless  to  add  that  this  does  not 
by  any  means  suggest  that  the  present  form  of  sol> 
darity  is  the  best  that  is  conceivable.  There  is  a 
perplexing  statement  in  this  connection  in  Professor 
Clark's  Distribution  of  Wealth : 1  — 

"  For  nothing,  if  not  to  protect  property,  does  the  state  exist. 
Hence  a  state  which  should  force  a  workman  to  leave  behind 
him  in  the  mill  property  that  was  his  by  right  of  creation, 
would  fail  at  a  critical  point.  A  study  of  distribution  settles 
this  question,  as  to  whether  the  modern  state  is  true  to  its 
principle.  Property  is  protected  at  the  point  of  its  origin,  if 
actual  wages  are  the  whole  product  of  labor,  if  interest  is  the 

1  Page  9. 


Conclusions  179 

product  of  capital,  and  if  profit  is  the  product  of  a  coordinating 
act." 

"When  this  introductory  statement  was  followed  by 
the  admirably  lucid  and  cogent  proof  with  which  we 
are  familiar  that  each  factor  in  production  does  tend 
to  get  what  it  produces,  one  could  scarcely  avoid 
a  sense  of  baffled  enthusiasm  in  recalling  the  words 
that  have  just  been  quoted. 

Of  course  the  solution  of  the  difficulty  lies  in  the 
apprehension  that  the  introductory  statement  and  the 
argument  take  for  granted  the  present  forms  of  own- 
ership of  property  and  the  present  social  and  technical 
conditions  of  production.  It  is  entirely  conceivable 
that  a  form  of  distribution  of  property  which  when 
tested  by  any  familiar  standard  of  equity  would  be 
pronounced  inequitable,  could  coexist  with  each  factor 
in  production  tending  to  get  what  it  produced.  The 
social  and  technical  conditions  of  production  might 
cooperate  to  reduce  the  national  dividend  to  a  mini- 
mum and  still  that  minimum  would  be  distributed 
according  to  the  specific  productivity  of  the  several 
factors. 

The  same  difficulty  takes  a  visible  form  in  the 
treatment  of  the  problem  of  production  and  distribu- 
tion by  a  series  of  simultaneous  equations,  as,  for 
example,  that  problem  is  treated  by  Professor  Mar- 
shall l  and  Professor  Pareto.2     The  problem  of  distribu- 

1  Marshall:  Principles  of  Economics,  4th  edit.  Appendix,  particu- 
larly notes  XIV,  XXI. 

-Pareto:  Count  ,r  economic  politique.  Vol.  I,  Principes  d'e'eonomie 
politique  pure. 


180  Laws  of  Wages 

tion  is  shown  to  be  determinate  if  the  following  facts 
are  known  :  (1)  the  effective  demand  schedules  of  the 
members  of  the  community,  which  result  from  their 
desires  and  their  wealth  ;  (2)  the  supply  schedules  of 
the  factors  of  production,  which  result  from  the 
amounts  of  the  factors  in  existence  and  the  needs  and 
dispositions  of  their  possessors;  (3)  the  functions 
descriptive  of  the  technical  conditions  of  production, 
which  depend  upon  the  state  of  invention  and  the 
legal  and  other  social  conditions  under  which  industry 
is  carried  on.  Whatever  may  be  the  character  of  the 
functions  of  these  three  items,  it  is  shown  that  under 
the  hypothesis  of  least  cost  or  of  perfect  competition, 
each  factor  will  tend  to  get  what  it  produces.  But 
that  fact  is  not  assumed  by  either  Professor  Marshall 
or  Professor  Pareto  to  be  any  justification  of  the  par- 
ticular forms  that  may  be  assumed  by  the  functions. 

This  observation  brings  us  to  a  perception  of  the 
further  practical  bearing  of  the  results  of  Chapter 
III.  In  order  that  the  problem  of  distribution  of 
income  may  be  determinate,  it  is  necessary  that  the 
number  of  equations  in  the  problem  shall  be  equal  to 
the  number  of  unknown  quantities.  Now  a  consider- 
able number  of  the  necessary  equations  are  dependent 
upon  the  proof  that  under  free  competition,  or  the 
hypothesis  of  least  cost,  each  factor  in  production 
gets  what  it  produces,  and  the  results  of  our  chapter 
show  that  so  far  as  labor  is  concerned  this  tends  to 
be  the  fact  in  the  present  industrial  organization  of 
society.     That  is   to    say,  an  important  part  —  but 


Conclusions  IM 

only  a  part,  let  it  be  understood1 — of  the  momentous 
problem  of  the  organization  of  industry  and  the  dis- 
tribution of  income  is  worked  out  as  it  should  be  in 
the  present  industrial  society. 

This  point  is  of  extreme  importance,  and  its  signifi- 
cance should  not  be  misunderstood.  There  are  two 
distinct  questions2  in  the  theory  of  the  socialization 
of  the  means  of  production:  (1)  as  to  whether  it  is 
socially  expedient  for  the  state  to  assume  control  of 
any  particular  form  of  the  means  of  production,  and 
(2)  as  to  the  principles  upon  which  the  ministry  of 
production  in  a  collectivist  state  should  organize  and 
carry  on  industry  with  the  means  of  production  placed 
at  its  disposal.  Postponing  the  discussion  of  the  firsl 
question  until  we  come  to  the  consideration  of  the 

1  Marshall  :  Principles  of  Economics,  4th  edit.,  p.  5S8. 

"Subject  to  conditions  which  are  indicated  in  the  foot-note,  hut 
are  not  important  for  our  main  purpose,  the  wages  of  every  class  of 
labour  tend  to  be  equal  to  the  net  product  due  to  the  additional 
labour  of  the  marginal  labourer  of  that  class. 

"  This  doctrine  has  sometimes  been  put  forward  as  a  theory  of  wages. 
In  reply  to  any  such  pretension,  it  may  be  objected  that  the  doctrine 
that,  the  earnings  of  a  worker  tend  to  be  equal  to  the  net  product  of 
his  work,  has  by  itself  no  real  meaning;  since  in  order  to  estimate 
Del  product,  we  have  to  take  for  granted  all  the  expenses  of  production 
of  the  commodity  on  which  he  works,  other  than  his  own  wages. 

••  Bui  though  this  objection  is  valid  against  a  claim  that  it  contains 
a  theory  of  wages,  it  is  not  valid  against  a  claim  that  the  doctrine 
throws  into  clear  light  the  action  of  one  of  the  causes  that  govern 
w  ages." 

-  In  this  paragraph,  I  follow  Professor  Barone,  who,  utilizing  the 
suggestions  of  the  earlier  work  of  Pare  to,  has  given  a  mathematical 
demonstration  of  the  proposition  under  discussion,  in  his  substantial 
articles  on  "II  ministro  della  produzione  nello  stato  collettivisto," 
which  were  published  in  the  Giornale  degli  Economisti,  L908,  pp.  267- 
293;  pp.  391-414. 


1$2  Laws  of  Wages 

results  of  another  chapter,  we  may  observe  that  if  in 
a  collectivist  state  the  minister  of  production  should 
seek  to  maximize  the  national  dividend  of  the  com- 
munity, he  must  so  apportion  the  means  of  production 
that  their  marginal  productivity  shall  be  the  same  in 
different  forms  of  production,  and  he  must  place  values 
upon  the  units  of  the  several  factors  that  are  propor- 
tionate to  their  respective  marginal  productivities. 
The  latter  principle  of  valuation  is  the  principle  of 
reward  according  to  specific  productivity  that  tends 
to  be  realized  in  the  present  industrial  state. 

In  reviewing  the  results  established  in  the  chapter 
on  "  Wages  and  Ability,"  we  shall  see  that  they  lend 
additional  force  to  what  has  just  been  said.  I  should 
like  first,  however,  to  amplify  an  idea  to  which  refer- 
ence was  made  a  moment  ago.  In  summarizing  the 
results  of  the  chapter  on  "  Wages  and  the  Standard 
of  Life,"  the  importance  of  distinguishing  in  theory 
between  the  qualities  of  different  groups  of  laborers 
was  dwelt  upon.  One  of  the  invaluable  services  that 
the  newer  statistical  methods  are  likely  to  render  to 
pure  economics  is  to  liberate  speculation  from  the 
bondage  to  the  average  in  which  it  has  labored  since 
the  beginning  of  the  science. 

The  syndicalist  Georges  Sorel  has  shown  how, 
influenced  by  the  special  conditions  of  production  in 
the  large  manufacturing  industries  of  England  and 
by  the  prevailing  forms  of  physical  science,  the  nine- 
teenth century  economists  disregarded  the  qualities 


Conclusions  L83 

that  differentiate  laborer  from  laborer  and  conducted 
their  reasoning  with  regard  to  "units  of  labor"  and 
"laborers  of  average  capacity." 

"On  arriva  ainsi  a  penser  que,  dans  Findustrie  la  plus 
avancee,  il  devenait  inutile  de  tenir  eompte  des  qualites  pro- 
pres  des  homines  et  qu'on  pouvait  considerer  les  travailleurs 
comme  des  atonies  de  quality  moyenne,  susceptible  d'etre 
seulement  distingues  par  des  grandeurs  mathematiques,  en 
sorte  que  toute  l'economie  devint  une  science  des  quantites  de 
travail  mises  en  jeu  par  les  capitalistes." 1 

The  most  marked  development  of  science  in  the 
latter  half  of  the  nineteenth  century  took  its  de- 
parture from  the  study  of  deviations  from  the  average 
rather  than  of  the  average  itself,  and  economists  will, 
of  course,  adjust  their  theories  in  the  light  of  this 
newer  evolutionary  science.  There  can  be  little  doubt 
that  egalitarian  doctrines  of  the  past  century  were 
fostered  through  the  inadequate  method  of  reasoning 
by  vaguely  conceived  averages  and  the  ignoring  of 
tlif  law  of  the  natural  differences  between  individuals 
in  any  large  group. 

That  there  is  a  law  of  natural  differences  between 
individuals  in  any  large  group,  no  one  who  is  ac- 
quainted with  the  results  of  recent  biometric  and 
anthropometric  work  will  deny.  The  point  that  con- 
cerns us,  however,  as  practical  economists  is  to  know 
whether  this  law  of  natural  differences  finds  its  ex- 
pression in  the  actual  earnings  of  laborers.  Accord- 
ing to  the  productivity  theory  of  wages  the  distribu- 
tion of  general  wages  among  the  groups  making  up 

1  Georges  Sorel :  Introduction  <i  l'economie  moderne,  p.  *_"•». 


184  Laws  of  Wages 

the  class  of  laborers  should  be  according  to  the  pro- 
ductive efficiency  of  the  respective  groups.  The  re- 
sults of  our  investigation  have  established  that  the 
law  of  the  natural  difference  in  ability  between 
individual  laborers  does  find  its  expression  in  the  ap- 
portionment of  earnings  among  laborers  in  the  present 
industrial  state,  and  that,  furthermore,  the  congruence 
is  remarkably  close  between  the  actual  distribution 
of  wages  and  distribution  as  it  should  be  according  to 
a  priori  theory. 

As  a  rule,  the  curve  descriptive  of  the  distribution 
of  wages  among  a  large  group  of  laborers  employed 
in  numerous  occupations  is  skew  in  a  positive  direc- 
tion. This  skewness  is  generally,  but  not  always,  a 
sign  of  improving  conditions  in  the  laboring  class. 
When  the  industry  grows  more  productive  and  earn- 
ings are  such  as  to  justify  an  increase  in  wages,  the 
more  intelligent  and  better  organized  laborers  are  the 
first  to  perceive  and  to  take  advantage  of  the  improved 
conditions.  The  more  prompt  adjustment  of  wages  of 
the  abler  laborers  to  the  increased  productivity  gives 
the  wages  curve  a  greater  measure  of  skewness.  The 
subsequent  changes  in  the  degrees  of  skewness  are  de- 
pendent upon  the  degree  of  friction  in  the  adjustment 
of  the  wages  of  the  less  able  laborers  and  upon  the 
improving  or  declining  general  conditions  of  industry. 

In  a  collectivist  state  conducted  upon  the  principle 
of  rendering  a  maximum  the  product  of  available 
labor  and  capital,  the  differences  of  earned  incomes 
of  the  members  of  the  state  must  conform  to  the  very 


Conclusions  185 

same  law  that  obtains  in  the  present  industrial  order. 
It  is  a  mark  of  the  great  progress  in  the  scientific 
treatment  of  social  questions  that  upon  this  funda- 
mental point  economist  and  socialist  are  in  agreement. 
Writing  under  the  influence  of  the  idea  of  Marx  thai 
is  quoted  as  the  motto  to  this  chapter,  Sorel  observes 
"  que  c'est  par  un  niecanisme  emprunte  a  l'ere  capital- 
iste  que  le  socialisme  compte  regler  la  repartition,"  ' 
and  then,  touching  upon  the  question  before  us,  he 
says:  " Le  capitalisme  .  .  .  tend  a  produire  une  cer- 
taine  egalisation  du  travail  entre  les  diverses  parties 
de  l'usine ;  mais  comme  il  a  besoin  d'un  nombre  con- 
siderable d'hommes  particulierement  actifs,  attentifs 
ou expriimentes,  il  s'ingenie  a  donner  des  supplements 
de  salaire  aux  hommes  qui  lui  rendent  ainsi  plus  de 
services ;  ce  n'est  point  par  des  considerations  de 
justice  qu'il  se  regie  dans  ce  calcul,  mais  par  la  seule 
recherche  empirique  d'un  equilibre  regie  par  les  prix. 
Le  capitalisme  arrive  done  a,  resoudre  un  problems 
qui  semblait  insoluble,  tant  qu'il  avait  ete  etudie  par 
les  utopistes ;  il  resout  la  question  de  l'egalite  des 
travailleurs,  tout  en  tenant  compte  des  inegalites 
naturelles  ou  acquises  qui  se  traduisent  par  des  ill- 
egal it es  dans  le  travail." 

The  only  "  socialist  revolution  "  of  which  we  have 
knowledge  is  the  revolution  in  the  opinions  of  lead- 
ing "scientific  socialists  "  2-- their   abandonment  of 


1  Soivl  :    I. a  Decomposition  du  Marxism?,  p.  41. 

2 The  right  to  refer  to  Sorel  as  a  socialist  can  scarcely  be  denied  in 
view  of  his  claim  to  teaching  le  Marxisme  de  Marx. 


186  Laws  of  Wages 

their  doctrine  of  the  cataclysmal  destruction  of  capi- 
talism and  their  apprehension  of  the  necessity  of  reg- 
ulating distribution  in  a  collectivist  state  by  means 
of  a  mechanism  borrowed  from  the  capitalist  era. 

The  most  critical  practical  questions  concerning 
the  income  of  laborers  are  the  questions  as  to  the 
effect  upon  wages  of  strikes  and  of  the  concentration 
of  industry  in  large  establishments.  It  is  by  means 
of  the  pressure  of  labor  organizations,  which  in  its 
acute  stage  takes  the  form  of  strikes,  that  laborers 
expect  to  compel  an  increase  of  wages ;  and  it  is  from 
the  growing  magnitude  of  the  aggregations  of  capital 
which  tend  more  and  more  to  control  the  output  in 
the  market  that  they  expect  to  find  their  greatest 
opposition.  These  two  subjects  form  the  topics  of 
our  last  two  chapters,  the  results  of  which,  as  to 
their  practical  bearings,  we  shall  consider  in  se- 
quence. 

Since  the  attitude  of  the  public  toward  industrial 
disputes,  in  the  matter  of  public  sympathy  and  public 
control,  must  change  with  the  degree  of  relevant 
scientific  information  that  is  available,  it  will  be 
well  to  consider  our  great  progress  during  the  last 
half  century  in  the  understanding  of  the  nature, 
causes,  and  effects  of  strikes. 

Fifty  years  ago  the  dominant  school  of  economists 
was  united  in  its  insistence  upon  a  vicious,  radi- 
cally fallacious  doctrine  of  wages  which  contained 
as  corollaries  :  — 


Conclusions  1S7 

(1)  the  doctrine  of  the  impotence  of  trades-union- 

ists to  increase  their  wages  through  combi- 
nations and  strikes  ; 

(2)  the  doctrine  of  the  impotence  of    laborers  to 

increase  their  wages  through  the  increase 
of  their  productive  efficiency  ; 

(3)  the  doctrine  of   the  impotence  of  laborers  to 

better  their  condition  by  exerting  pressure, 
through  combination,  upon  the  employers 
to  the  end  that  they  should  increase  the 
efficiency  of  their  plant  and  organization. 

This  theory  of  wages  was  so  hypothetical  and  so 
vague  that  it  was  impossible  to  put  it  to  an  inductive 
test.  Indeed  the  nebulous  character  of  the  theory  was 
one  condition  of  its  persistence ;  for,  as  soon  as  pre- 
cision was  given  to  the  terms  in  which  it  was  ex- 
pressed, it  was  seen  that  the  modicum  of  truth  in 
the  doctrine  was  but  little  more  than  a  pedantic 
elaboration  of  a  platitude. 

The  successful  middle  class  that  had  risen  in  wealth 
and  power  during  the  period  following  the  industrial 
revolution  was  predisposed,  in  consequence  of  its 
industrial  interests,  to  accept  the  economic  doctrine 
of  the  wa gres-fund  with  all  of  its  corollaries.  Accord- 
ingly,  strikes  and  labor  combinations  were  regarded 
as  being  impotent  to  achieve  the  effects  sought  by 
trades-unionists  and  as  being,  moreover,  conspiracies 
against  public  order.  In  the  meanwhile  strikes  in- 
creased in  number  and  extent  and  bitterness  of  con- 


lss  Laws  of  Wages 

flict,  and,  notwithstanding  the  enormous  public 
interests  at  stake,  no  public  authority  concerned 
itself  with  the  collection  of  adequate  material  hear- 
ing upon  the  origin,  causes,  and  outcome  of  strikes, 
which  material  alone,  when  properly  interpreted, 
could  possibly  afford  guidance  in  the  direction  and 
control  of  this  form  of  industrial  warfare. 

During  the  interval  of  fifty  years,  the  progress  in 
the  understanding  of  the  labor  question  has  been 
such  as  to  lead  to  a  reversal  of  attitude  upon  all  of 
these  points.  A  new  theory  of  wages,  definite  in 
form  and  admitting  of  empirical  tests,  has  been 
developed  as  a  part  of  a  general  efficiency  theory  of 
distribution.  80  far  as  its  fundamental  propositions 
have  been  tested  it  has  been  found  that  the  theory 
tends  to  be  realized  in  actual  practice.  The  essential 
idea  of  the  new  doctrine  is  that,  with  a  definite  tech- 
nical and  social  organization  of  industry,  the  laborer 
tends  to  get  what  he  produces.  Corollaries  to  the 
doctrine  are :  — 

(1)  that  whatever  leads  to  an  increase  in  the  effi- 

ciency of  the  worker  will  tend  to  increase  his 
.    wages ; 

(2)  that  if  increased  wages  do  not  follow  upon  in- 

creased efficiency  of  the  industrial  worker, 
the  labor  combinations  can,  through  strikes, 
force  the  cession  of  the  increased  product ; 

(3)  that  without  the  increased  efficiency  no  amount 

of  striking  will  result  in  a  permanent  increase 
of  wages  ; 


Conclusions  L89 

(4)  that  labor  organizations,  through  their  powers 
of  putting   pressure  upon   the  employer  to 

increase  the  efficiency  of  his  plant  and  or- 
ganization, have  a  means  not  only  of  in- 
creasing wages,  but  of  enlarging  the  national 

dividend. 

Public  opinion  is  in  the  process  of  adjusting  itself 
to  the  new  light.  The  vagaries  of  early  economists 
have  discredited  a  priori  opinions  as  to  industrial 
matters ;  it  is  insisted  that  economic  truths  like  all 
other  truths  can  be  reached  only  by  treating  scien- 
tifically the  relevant  facts  that  are  laboriously  accu- 
mulated. Accordingly,  in  nearly  all  of  the  states  of 
Europe,  public  bureaus  have  been  established  for  the 
purpose  of  collecting  and  interpreting  the  facts  bear- 
ing upon  the  labor  question. 

The  material  available  at  present  is  neither  satis- 
factory in  classification  nor  adequate  in  amount  for 
a  complete  treatment  of  the  question  of  strikes.  But 
the  results  in  Chapter  V  show  — 

(1)  that  the  outcome  of  strikes  is  subject  to  statisti- 

cal and  economic  laws  ; 

(2)  that  the    scientific    apparatus    in  the  form  of 

economic  theory  and  statistical  mathematics 
has  been  developed  to  such  a  degree  of  power 
as  to  be  equal  to  the  handling  of  this  com- 
plex problem  ; 

(3)  that  there  is  reason  for  believing  that  if  data 

of    satisfactory   quality   and    quantity    were 


190  Laws  of  Wages 

supplied,  the  whole  subject  could  be  placed 
upon  a  scientific  foundation  admitting  of  the 
prediction  of  average  results  in  a  way  that 
would  approximate  the  actuarial  calculations 
of  life  insurance. 

Public  opinion,  as  has  been  said,  is  adjusting  itself 
to  the  newer  light.  Public  opinion  is  unalterable  in  its 
condemnation  of  the  form  of  industrial  treason  that 
is  manifested  in  a  general  strike.  Its  condemnation 
is  unalterable  because  there  is  absolute  certainty  that 
no  economic  service  rendered  by  the  aggrieved  class 
is  comparable  to  the  economic  loss  that  would  follow 
upon  a  tolerated  general  strike.  Public  opinion  is  in 
sympathy  with  or  in  opposition  to  strikers  according 
as  it  is  made  clear  that  the  strikers  have  or  have  not 
created  a  value  that  is  appropriated  by  the  employer. 
It  would  therefore  seem  obvious  that  since  public 
opinion  does  utilize  the  degree  of  knowledge  that  is 
available,  and  since  adequate  scientific  knowledge 
could  be  supplied,  if  only  the  facts  were  properly 
collected  and  analyzed,  we  should  not  be  far  from  the 
solution  of  a  problem  that  many  have  regarded  as  in- 
soluble. Our  progress  during  the  last  fifty  years 
justifies  this  belief ;  the  importance  of  the  question 
justifies  the  exertion  of  any  degree  of  pressure  upon 
an  industrial  group  that  should  either  withhold  the 
facts,  or  pollute  the  sources  of  knowledge  for  the 
purpose  of  exploiting  an  opportunity  created  by  public 
ignorance  or  misinformation. 


Conclusions  I'M 

In  the  matter  of  the  attitude  of  the  state  toward 
economic  activities,  we  have  made  the  distinction  ' 
between  the  question  (1)  as  to  what  forms  of  capital 
should  be  socialized,  and  (2)  as  to  the  principles  thai 
must  be  followed  by  a  collectivist  minister  in  the  direc- 
tion of  production  and  distribution.  With  regard  to 
the  latter  question  it  has  been  shown  to  be  demonstrable 
that,  if  a  collectivist  state  is  to  have  any  degree  of 
stability, the  principles  followed  in  the  apportionment 
of  labor  and  capital  in  production  and  in  the  distri- 
bution of  the  product  of  industry  must  be  the  same 
in  the  collectivist  state  as  in  the  present  industrial 
state,  and  that  when  recent  socialist  thinkers  have 
attempted  to  give  definiteness  to  their  proposals  for 
collective  control  and  administration,  they  admit  this 
fact.  We  have  further  shown  that  when  conrpetition 
tends  to  be  realized — in  the  technical  sense  of  the 
word  competition  —  or  when  through  collective  bar- 
gaining results  approximating  competitive  standards 
are  reached,  the  presumption  is  against  any  attempt 
at  socialization  of  the  industry  concerned. 

The  results  of  Chapter  V 1  on  "  Wages  and  the 
Concentration  of  Industry ,:  will  throw  some  light 
on  the  first  of  the  two  questions  into  which  we 
have  divided  the  problem  of  socialization  ;  viz..  what 
tonus  of  capital  should  be  socialized.  As  we  have 
shown  that  the  presumption  is  in  favor  of  the  present 
order  of  production  when  competitive  standards  are 

1  Barone  made  the  distinction  in  1908  in  his  articles  on  ••  II  mi- 
nistro  della  produzione  nello  stato  collettivisto." 


L92  Laws  of  Wages 

realized,  it  is  quite  clear  that  the  ground  for  belief  in 
the  expediency  of  socializing  any  form  of  concentrated 
industry  must  be  found  in  the  deviation  of  the  facts 
of  industry  where  concentration  obtains  from  the 
standards  that  would  be  realized  under  competitive 
conditions.  We  are  therefore  led  to  inquire  in  what 
respect,  so  far  as  the  laborer  is  concerned,  do  the 
facts  of  industry  where  masses  of  capital  and  labor 
are  aggregated  differ  from  the  facts  where  labor  and 
capital  cooperate  in  the  same  industry  upon  a  smaller 
scale.  Concentration  of  industry,  in  the  sense  in 
which  the  term  is  used  here,  viz.,  of  aggregation  of 
capital  and  labor  in  the  same  establishment,  does  not 
by  any  means  imply  the  abrogation  of  competition. 
But  it  is  a  normal  form  of  transition  from  competi- 
tion to  monopoly  and  for  that  reason  deserves  especial 
investigation. 

The  researches  of  Chapter  VI  have  been  under- 
taken with  a  view  to  discovering  the  effects  of  con- 
centration of  industry  upon  the  status  of  the  laborer. 
The  broad  general  results  of  the  chapter  are 1  — 

1  A  technical  detail  affecting  the  comparison  of  the  wages  received 
in  large  and  in  small  establishments  is  of  sufficient  importance  to 
justify. a  note. 

When  such  comparisons  are  made,  spurious  differences  that  are 
due  to  several  causes  are  obtained.  A  common  form  of  spurious  dif- 
ferences has  its  origin  in  the  lumping  together  of  wage  statistics  from 
different  geographical  districts,  as,  for  example,  when  the  wages  paid 
in  l he  manufacture  of  cotton  in  the  northern  and  southern  states  of 
the  United  States  are  massed  in  a  classification  of  rates  of  wages  ac- 
cording to  the  size  of  establishments  (cf.  Earnings  of  Wage-earners, 
Census  of  Manufactures,  1905,  Bulletin  93,  pp.  73-81).  In  this  case, 
a  comparison  between  the  mean  rate  of  wages  in  large  establishments 


Conclusions  1 '.  ».' ! 

(1)  That  as  regards  the  four  critical  items  —  rate 

of  wages,  amount  of  employment,  continuity 
of  employment,  and  length  of  the  working 
day,  the  status  of  the  laborer  improves  with 
the  increasing  concentration  of  industry ; 

(2)  That  the  greater  complexity  of  production  fol- 

lowing upon  the  concentration  of  labor  and 
capital  creates  new  opportunities  for  efficient 
laborers  to  exploit  their  differential  ability ; 

(3)  That,  when  the  degree  of  the  concentration  of 

industry  increases,  the  similarity  and  the 
differences  in  the  operation  of  the  law  of 
the  variation  of  wages  with  the  age  of  the 

and  the  mean  rate  in  small  establishments  would  show  a  difference 
in  favor  of  large  establishments.  But  this  difference  would  be  spu- 
rious so  far  as  concerns  the  effect  of  the  size  of  the  establishment 
upon  the  rate  of  wages.  The  fact  that  the  large  establishments  are 
situated  in  greater  number  in  the  northern  states  where  a  high  rate 
of  wages  prevails  would  be  an  explanation  of  a  difference  in  the  rate 
of  wages  paid  in  the  large  and  in  the  small  establishments. 

A  more  subtle  form  of  spurious  difference  is  manifested  when 
wage  statistics  are  presented  without  reference  to  the  age  grouping  of 
the  laborers.  That  is  to  say,  increasing  concentration  of  industry 
implies  a  form  of  industrial  selection  of  laborers  which  shows  itself, 
in  one  way,  by  the  different  age  groupings  of  laborers  in  large  and  in 
small  establishments. 

The  constants  in  the  equation  expressing  the  law  of  the  variation 
of  wages  with  age  vary  not  only  with  the  degrees  of  concentration  of 
capital  and  labor  in  the  same  industry  but  also  from  industry  to  in- 
dustry. In  both  cases  these  variations  should  be  taken  into  accounl 
before  comparisons  are  instituted  between  the  rates  of  wages  in  dif- 
ferent industries  and  in  establishments  varying  in  size  in  the  same 
industry.  It  is  suggested  that  in  the  presentation  of  wage  statistics 
a  plan  should  be  followed  similar  to  the  procedure  of  the  Knglish 
Registrar  (Jeneral,  in  his  comparison  of  death  rates  in  different  plaC(  S 
where  the  age  groupings  of  the  populations  are  different. 

o 


194  Laws  of  Wages 

worker  are  explicable  by  means  of  the 
hypothesis  that  the  laborer  tends  to  earn 
an  income  proportionate  to  his  efficiency  in 
production. 

These  inductive  findings  not  only  reenforce  the 
belief  that,  so  far  as  the  welfare  of  the  laborer  is  con- 
cerned, concentration  of  industry  is  no  ground  for 
the  socialization  of  industry,  but  they  place  in  clearer 
light  the  solidarity  of  industry  and  illustrate  how  the 
increasing  welfare  of  the  laborer  is  dependent  upon 
the  skillful  management  of  large  capital. 

We  finally  reach  our  question  as  to  what  forms  of 
capital  or  economic  institutions  should  be  socialized, 
meaning  by  socialization  the  administration  in  the 
common  interest  of  society.  We  need  a  principle 
upon  which  to  make  the  decision,  and  we  need  a 
method  by  which  each  institution  may  be  put  to  the 
test  of  our  principle. 

In  our  quest  of  a  principle  we  may  start  from  two 
propositions  which  I  think  will  be  accepted  by  both 
economist  and  socialist.  We  may  assume  first,  that, 
so  far  as  it  is  compatible  with  the  acquisition  of 
better  things,  it  is  desirable  to  have  the  national 
dividend  of  wealth  a  maximum ;  and,  secondly,  that 
those  who  take  part  in  the  creation  of  the  dividend 
should  receive  shares  that  are  proportionate  to  their 
contribution  to  the  total  product.  Our  principle  is 
implicit  in  these  propositions,  and  it  may  be  worded 
as  follows :  the  economic  resources  of  a  state  should 


Conclusions  L95 

be  so  utilized  as  to  render  the  national  dividend  of 
wealth  the  maximum  that  is  compatible  with  the 
acquisition  of  better  things,  and  the  dividend  should 
be  so  distributed  that  each  contributor  to  its  pro- 
duction should  receive  a  share  proportionate  to  his 
services. 

The  method  of  applying  this  test  of  an  efficient 
economy  is  a  combination  of  synthetic  economics1 
and  statistical  economics.  We  have  shown  in  an 
earlier  part  of  this  chapter  that,  according  to  recent 
economic  theory,  the  problem  of  production  and  dis- 
tribution of  wealth  is  determinate,  if  we  admit  the 
hypothesis  of  least  cost  or  of  perfect  competition  and 
have  a  knowledge  of  three  facts:  (1)  the  effective 
demand  schedules  of  the  members  of  the  community, 
which  result  from  their  desires  and  their  wealth  ; 
(2)  the  supply  schedules  of  the  factors  in  production, 
which  result  from  the  amounts  of  the  factors  in 
existence  and  the  needs  and  dispositions  of  their 
possessors ;  (3)  the  functions  descriptive  of  the 
technical  conditions  of  production,  which  are  depend- 
ent upon  the  state  of  invention  and  the  legal  and 
other  social  conditions  under  which  industry  is  carried 
on.  Starting  from  this  hypothesis  and  the  knowledge 
of  these  three  facts,  it  may  be  proved  that  undez  t]w 
assumed  con dit ions  the  national  dividend  isamaximum 
ami  ike  owners  <>f  the  factors  of  production    arc   re- 


1  Barone  refers  to  the  type  of  economic  theory  in  which  the  conditions 
of  production  and  distribution  an-  simultaneously  presented  in  a 
series  of  equations  as  L'economia  sintetica. 


196  Laws  of  Wages 

warded  with  shares  proportionate  to  the  contributions 
of  the  several  factors  to  the  production  of  the  dividend. 
The  words  that' are  italicized  in  the  preceding  de- 
scription are  critical  for  the  application  of  the  test  of 
an  efficient  economy.  The  test  requires  that  the  re- 
sources of  the  state  shall  be  so  utilized  as  to  render 
the  national  dividend  the  maximum  that  is  compatible 
with  the  acquisition  of  better  things,  whereas  in  the 
above  economy,  the  national  dividend  is  rendered  a 
maximum  under  the  assumed  rights  of  ownership  of 
the  factors  of  production  and  the  existing  technical, 
legal,  and  other  social  conditions  of  production. 
Furthermore,  the  test  requires  that  the  individuals  in 
the  community  should  receive  shares  of  the  dividend 
proportionate  to  their  contributions  in  its  production, 
whereas  the  above  economy  cedes  to  the  owners  of 
the  factors  of  production  shares  proportionate  to  the 
contributions  of  the  factors.  Whether,  in  these  two 
points,  there  is  a  great  or  small  discrepancy  between 
the  ideal  and  the  actual  depends  upon  the  concrete 
form  of  the  premises  upon  which  the  theory  rests. 
It  is  the  task  of  synthetic  economics  to  supply  a 
general  solution  of  the  problem  as  to  the  effects  upon 
the  size  of  the  national  dividend  and  its  resulting 
distribution  of  any  alteration  in  the  hypotheses  or  the 
premises  upon  which  the  theory  rests.  It  is  the  task 
of  statistical  economics  to  give  concrete  form  to  the 
premises  and  the  general  solution  by  summarizing  in 
mathematical  form  the  relevant  facts  in  the  present 
order  of  production  and  distribution. 


HPHE    following   pages  contain  advertisements   of  a  few 
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The  Law  of  the  Employment 
of  Labor 

By  L.  D.  CLARK 

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In  all  the  realm  of  economics  it  is  strange  that  heretofore  no  book  has 
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phases  as  well  as  the  nature  and  trend  of  legislation  are  discussed  and 
illustrated  in  so  far  as  these  are  applicable  to  workmen  and  their 
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By  SCOTT   NEARING,    Ph.D. 

Of  the  Wharton  School,  University  of  Pennsylvania 

Social  Adjustment 

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Wages  in  the  United  States 

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THE    MACMILLAN    COMPANY 

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PRINCIPLES    OF    ECONOMICS 

By  F.  W.  TAUSSIG 

Henry  Lee  Professor  of  Economics  in  Harvard  University 

Cloth,  Svo,  2  volumes,  $4.00  net  per  set 

This  book,  which  is  addressed  neither  to  specialists  nor  to  chil- 
dren, but  to  students  and  the  educated  public,  states  simply  but 
fully  the  main  principles  of  economics  and  their  application.  It 
does  not  avoid  difficult  or  severe  reasoning,  but  centers  attention 
on  the  larger  problems  and  the  important  trains  of  reasoning  and 
treats  these  liberally  and  fully.  The  book  deals  with  the  present 
day  ;  there  is  very  little  of  economic  history,  very  little  about  the 
phenomena  of  semi-civilization  or  barbarian  society.  The  expe- 
riences and  problems  of  countries  of  advanced  civilization  are  pri- 
marily kept  in  view.  American  problems  naturally  receive  con- 
siderable attention,  but  the  author  is  chiefly  concerned  with  those 
principles  which  are  of  general  application  in  all  of  the  leading 
countries  of  modern  times. 


ECONOMICS 

By  SCOTT    NEARING  and  FRANK   D.  WATSON 

Both  instructors  in  Political  Economy  in  the  Wharton  School  of  Finance  and 
Commerce,  University  of  Pennsylvania 

Cloth,  8vo,  4Q3  pages,  $i.go  net 

The  book  discusses  the  whole  subject  of  prosperity  of  the  factors 
which  enter  into  the  complex  economic  life  of  the  nation.  A 
young  man  who  wishes  to  read  even  the  daily  paper  with  full  in- 
telligence would  find  time  spent  in  reading  this  book  well  em- 
ployed for  the  help  which  it  would  give  him  in  understanding 
current  discussions  of  such  topics  as  the  standard  of  living ;  the 
natural  resources  of  the  country  and  their  conservation ;  the 
relations  of  labor  and  immigration  ;  of  the  labor  of  women  and 
children  to  industrial  progress;  of  organization  in  business  and 
its  tendencies  ;  of  the  growth  and  functions  of  large  corporations  ; 
of  public  ownership ;  of  the  various  experiments  which  have  been 
tried  at  different  times,  or  the  programmes  which  social  leaders 
are  now  proposing  for  the  remedy  or  the  prevention  of  economic 
injustice.  

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Law  for  the  American  Farmer 

By  JOHN    B.  GREEN,  of  the  New  York  Bar 

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"  A  volume  that  bears  the  marks  of  painstaking  effort  to  present 
information  that  will  be  useful  to  those  engaged  in  agriculture. 
In  no  sense  is  the  book  intended  to  take  the  place  of  counsel, 
but  merely  to  fit  the  owner  of  a  farm  to  cope  with  legal  ques- 
tions which  may  arise  any  day  in  the  conduct  of  his  farm. 
Any  person  who  will  make  himself  familiar  with  the  contents 
of  this  book  will  possess  a  liberal  education." — Boston  Globe. 

A  Living  Wage  :    Its  Ethical  and  Economic  Aspects 

By  Rev.  J.  A.  RYAN.  Cloth,  \21no,  $1.00  net ;  by  mail,  $1.12 
"  A  clear  and  concise  study  of  the  wage  problem." 

The  Labor  Movement  in  America 

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A  historical  and  critical  sketch  of  the  struggle  of  the  day-by- 
day  working  population  of  North  America  for  the  betterment 
of  their  condition. 

Labor  Problems 

By  THOMAS  S.  ADAMS  and  HELEN  L.  SUMNER 

87 'o,  cloth,  gilt  top,  $1.60  net 

"  Invaluable  as  presenting  in  convenient  and  accessible  form 
necessary  material  that  would  else  have  to  be  searched  for  in 
widely  scattered  sources."  —  Providence  Journal. 

Federal  Power  over  Carriers  and  Corporations  : 

A  Study  of  the  Sherman  Anti-Trust  Law 

By  E.  PARMALEE  PRENTICE.  i2mo,  cloth.  Si. 50  net 

This  is  an  exhaustive  study  of  the  Sherman  Anti-Trust  Act 
and  of  the  Federal  powers  upon  which  the  Act  is  based. 


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Wage-Earning  Women 

By  ANNIE    MARION    MacLEAN 

Professor  of  Sociology  in  Adelphi  College 

Cloth,  leather  back,  i2mo,  $1.25  net;  by  mail,  $1.35 

"This  book  needed  to  be  written.  Society  has  to  be  re- 
minded that  the  prime  function  of  women  must  ever  be 
the  perpetuation  of  the  race.  It  can  be  so  reminded  only 
by  a  startling  presentation  of  the  woman  who  is  '  speeded 
up  '  on  a  machine,  the  woman  who  breaks  records  in  pack- 
ing prunes  or  picking  hops,  the  woman  who  outdoes  all 
others  in  vamping  shoes  or  spooling  cotton.  .  .  .  The  chap- 
ters give  glimpses  of  women  wage-earners  as  they  toil  in  dif- 
ferent parts  of  the  country.  The  author  visited  the  shoe- 
shops,  and  the  paper,  cotton,  and  woollen  mills  of  New 
England,  the  department  stores  of  Chicago,  the  garment- 
makers'  homes  in  New  York,  the  silk  mills  and  potteries 
of  New  Jersey,  the  fruit  farms  of  California,  the  coal  fields 
of  Pennsylvania,  and  the  hop  industries  of  Oregon.  The 
author  calls  for  legislation  regardless  of  constitutional 
quibble,  for  a  shorter  work-day,  a  higher  wage,  the  estab- 
lishment of  residential  clubs,  the  closer  cooperation  between 
existing  organizations  for  industrial  betterment." 

—  B os ton  Advertiser. 

Making  Both  Ends  Meet : 

The  Income  and  Outlay  of  Ne<w  York  Working  Girls 
By  SUE    AINSLIE    CLARK  and  EDITH    WYATT 

Illustrated,  cloth,  i2mo,  270  pages,  $1.50  net;  by  mail,  $1.60 

The  girl  who,  without  friends  or  home,  is  obliged  to  earn 
her  living  in  a  big  city,  faces  a  very  real  problem.  Vari- 
ous phases  of  this  problem  have  been  dealt  with  by  phil- 
anthropic, social  and  religious  workers  and  writers,  but 
the  solution  is  seemingly  as  far  away  as  ever.  Though 
there  are  many  homes  and  organizations  of  a  semi-chari- 
table nature  in  all  our  large  cities,  these  really  can  care  for 
and  watch  over  but  a  small  per  cent  of  the  working  girl 
population.  Those  who  for  one  reason  or  another  do  not 
come  within  the  radius  of  these  institutions  must  shift  en- 
tirely for  themselves.  These  are  the  subjects  of  Mrs. 
Clark  and  Miss  Wyatt's  book. 


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American  Social  Progress  Series 

Edited  by 
Professor    SAMUEL     McCUNE    LINDSAY,    Ph.D.,    LL.D., 

Columbia  University 


A  series  of  handbooks  for  the  student  and  general  reader,  giving 
the  results  of  the  newer  social  thought  and  of  recent  scientific  in- 
vestigations of  the  facts  of  American  social  life  and  institutions. 
Each  volume  about  200  pages. 

1  — The  New  Basis  of  Civilization.    By  Simon  N.  Patten,  Ph.D., 

LL.D.,  University  of  Pennsylvania.     Price,  $1.00  net. 

2  —  Standards  of  Public  Morality.     By  Arthur  Twining  Had- 

ley,   Ph.D.,  LL.D.,  President  of  Yale   University.     Price, 
Si .00  net. 

3  —  Misery   and   Its   Causes.     By  Edward   T.  Devine,  Ph.D., 

LL.D.,  Columbia  University.     Price,  $1.25  net. 

4  —  Government  Action  for  Social  Welfare.     By  Jeremiah  W. 

If.nks.  Ph.D.,  LL.D.,  Cornell  University.     Price,  $1.00  net. 

5  —  Social  Insurance.    A  Program  of  Social  Reform.    By  Henry 

Rogers  Seager,  Ph.D.,  Columbia  University.     Price,  $1.00 
net. 

6  —  The  Social  Basis  of  Religion.     By  Simon  N.  Patten,  Ph.D.. 

LL.D.,  University  of  Pennsylvania.     Price,  J1.25  net. 

j  —  Social  Reform  and  the  Constitution.    By  Frank  J.  Goodn<  >w, 
LL.D.,  Columbia  University.     Cloth,  121110,  $1-50  net. 


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